 okay and that was so we took an hour almost so we can go to part two like I said we almost like almost over with time we can extend the time and those who wants to leave they can leave I will post their videos I will post the videos because then it will take us longer to do all of them so that then makes it easier and quicker to I will post them I'm not sure maybe later today I will download them and then post them okay so let's any question so far as you can see that it took us longer together to do only part one remember you have only an hour in the exam to answer part one and you have an hour to answer part two so in the exam you will not have me explaining concepts you just have yourself and teach in the box it will take you less time because you're not going to go through exactly the same thing that I am going to move with you okay so let's do part one part one asks this is now we move into sampling distribution questions sampling distribution questions they give you the mean they give you the standard deviation and they tell you what your sample size is and what they are asking remember you see the mean the standard deviations and all that so in your cheat sheet the name you would appreciate sampling distribution from for the mean and with the mean you will have your standard error formula and the probability formula your standard sampling distribution formula your z school so what your standard error you will write you would have written it like that which tells me the standard error for the mean and this is your population standard deviation divided by the square root of your sample size just take your standard deviation which is a thousand divided by the sample size which is a 10,000 12 of 10,000 and you will have to take your sample your standard error where is she and what do you get the answer is option A you write it on Monday so whatever I'm saying today I hope you are following it write a cheat sheet with your chapters and the formulas that relates to that so that the exam really available for you I know I'm going to get into trouble because your lectures also listen to this recording I am giving you advice here but you just need to make sure that this is a one time offer because next year you fail and you start next year next day there will be a proper when you write in the exam therefore it means somebody will be looking at what you are doing you will have to do a 360 the view of your area to show that there is no piece of paper anyway and you write your exam like that so this is a one time opportunity for you to pass this and to do that I am giving you that so you must you must do that write a cheat sheet formula with all the formulas that you will need per chapter and highlighting which chapter makes life easier and in the table as well so the table you just open it you have it ready open on the side so remember it will not be on your my you need so you will have your my my one product my exam open so you cannot download the exam paper as well so you will have your your my exam open up you can always go back so because it will be in Google and you can always talk between your Explorer and your PDF document in that way okay so going forward the next question also continues so in this exam they gave you only one question from from something this is wish so this will be a question from confidence interval and all these are hints like you just need to make sure that you know what you know that the other thing that you also need to make when you do this for confidence interval you remember the table I shared with you to say critical values and we have the z alpha divided by two values and all that you can write the critical values table so you will go and create your critical value and say this is more for my z alpha divided by two and this will be for my z alpha and then yeah you will say at 95 percent confidence interval what will be my critical weight one comma nine six at my 90 it will be one comma six four five because for 95 confidence interval it will be different for z alpha and this will be one comma six four five something like that so but you will need to use the correct confidence intervals right there okay so I'm going to give you a shortcut because we always remember for a 95 percent confidence interval the z critical value alpha divided by two will always be one comma nine six you know that we're doing the mean the confidence interval for the mean because this is the population mean therefore the formula is your point estimate plus or minus the critical value of z alpha divided by two times the standard error which is your population standard deviation divided by the square root of n so now we know what our mean is we know what our standard deviation is other thing sorry I forgot to mention this they give us the sample standard deviation for the mean oh let's go back oh this is going to be very interesting for the mean you need to read the question correctly and carefully so I've given you wrong information right now right here with this so population standard deviation which is sigma is known then we use z if the population standard deviation which is sigma unknown so this is known and this is unknown if it's unknown we use t so when it's unknown it means they give us the sample standard deviation sorry my bad so since this is a sample standard deviation we're going to be using t alpha divided by two and the degrees of freedom we need to remember all those things we need to remember that so at 95 so we know that this will be one minus alpha is equals to zero comma nine five which means therefore our alpha is zero comma zero five so our degrees of freedom which is n minus one it's relying on that so it will be 70 minus one that is our degrees of freedom which will be 69 so our three alpha alpha divided by two so if we divide alpha divided by two we get zero comma zero two five and our degrees of freedom of 67 so you need to go to the t table the graph below is 69 69 oh sorry because we are looking at 67 69 so we go to the t table so we go t table and this is the critical values of t and we look for the degrees of freedom then our alpha right sorry our t alpha of zero comma zero two five which is that column number one two three four because when I scroll up it's going to disappear column number four so we go down down down down down down down down down down so continue to critical values of t and we look for 69. And there is our 69 and our T value is that. One, two, three. And we'll do that. So please pay attention. What your critical value will have been given in the exam because it might give you 60, 50, 40 different different N values. Or they might give you different questions. So pay attention to your one that you are doing. But yeah, I'm just giving you a few things on how to answer the question. So one comma 9, 9, 4, 9. So our critical value here is one comma. 9, 9, 9, 4. 9, 9, 4, 9. 9, 9, 4, 9. That is our critical value. So now we can calculate our confidence in cover. Point estimate plus or minus T alpha divided by 2 and the degrees of freedom and our sample standard deviation divided by the square root of N. Our sample size is 3, 7, 3, 0. Plus or minus our critical value. We calculated it. It was one comma 9, 9, 4, 9. Thanks. Our standard error. Sample standard deviation is 1,000 divided by the square root of 70. I'm also going to calculate it from my side. Please calculate it on your side so that you can compare our answers. 1,000 divided by the square root of 70 equals 1, 1, 9. Some number multiplied by 1, 9, 9, 4, 9. Equals. And I'm going correct here. Plus or minus 2, 3, 8, 4, 3, 6, 2. Because my calculator is in four decimal places. I'm going to keep it at four decimal places. 3, 7, 3, 0. Now here I can just split it. 3, 7, 3, 0. Minus 2, 3, 8, 4, 3, 6, 2. And 3, 7, 3, 0, minus 2, 3, 8, 4, 3, 6, 2. It's 3, 3, 4, 9, 1, 5, 6. And I think because they rounded off to a whole number, so we can also round it off. 3, 9, it will be the same as 3, 9, 2. Because the other thing, we look at what the options look like. So the options are whole number. So we can also keep our answer as a whole number. And the next answer will be 3, 9, 6, 8, 4, 3, 6, 2. So which is option number? 3, 9, 6, 2. That's how you will answer that question. Ma'am, can I ask something? Yes. The 0 point on top up there, the 0.95. Where do we get these values? And 0, 0.05. OK. So a 95% confidence level is equivalent to 1 minus 0.95, which is 95 divided by 100. Remember that? Yeah. 95 divided by 100 is 0.95. So 0.95, we can write it as 1 minus alpha. And if you make alpha the subject of the formula, 1 minus alpha will be equal to 0.95. I move alpha the site, and I move 0.95. The site will be minus 0.95. And to solve this, 1 minus 0.95 is 0.05 alpha. And this gives me 0.005, which is that. To get the critical value of 0.25 is the alpha divided by 2, which is 0.05 divided by 2, which is as 0.0250, which is the answer we got there. I applied shortcut because I assumed that you know this from the start of the day. OK. Thank you so much. No problem. Moving to the next one, it's also confidence intervals. So yes, you also need to read the question carefully. The minute you don't see anything about standard deviation or the mean, you must know that this is confidence interval for the proportion. So here in the statement, if you read, then it didn't give you anything about the mean. So this is proportion. We're still doing confidence interval because if you look at this, the statement still states that confidence interval. And it says construct a 99% confidence interval. A 99% confidence interval, it means it's 1 minus alpha of 0.999. Therefore, it means our alpha is 0.01. And since this is proportion, and for proportion, we always use z. So we use p plus or minus our point estimate, which is the sample proportions. The critical value will be z alpha divided by 2. Our standard error will be the square root of your p 1 minus your sample proportion divided by n. Now, remember also, if you use your sample proportion, they would have given you your n. The study shows, which is our n, then commercial landlords shows that 80 of them have reduced their rentals. So our n, which is 80, divided by our n of 200, gives us our sample proportion. So what we get divided by 200 is 0.40. 0.40 plus or minus our critical value, you need to go find it on the t table. So it's on the z of 0.01 divided by 2, which is z of 0.00. For those who don't know where to find it, so 0.01 divided by 2 is that 0.00. How we find it on the table? So there are two ways. If you have created yourself, that's the digital bin table. If you created it for yourself, then you don't have to work too much about where to find the z, how to find the z, the critical bin. But I'm going to show you on the... So this is the table that you can create for yourself. So I'm not sure if you are able to see this. I'm going to leave it here for some time, so take it up. Thank you. Regardless of the z, alpha divided by 2 or z, so we can use that alpha divided by 2 or z, alpha. As long as you can see there, but the 0.005 number, they do. So we're looking for a 99% and we know that at 99% it's 0.005, so therefore that will be the probability. But this we always say 2.58. Keep it at 2 decimal, 2.58. The only exception is that one. So this is 2.58, so you must have it as that. Did you write this table down? Did you do coffee? Out of it, but I'm going to show you how to find the same value on your table. Can I move? No. Go back to the normal distribution table. You go there, you always use the z, the negative side of the table. Inside the table we are looking for a value. We are looking for 0.005. So it will look for 0.05. This is 0.059, so my bad. So we're looking for 0.005. And this can be our answer. And if we go out, it corresponds to z of minus 2.5 at the top, that's sort of on the left, and 0.58 on the right. And that's how you will find the critical value. So we know that our critical value is 2.58 for this. So if you don't come and you don't come, it's 2.58 hours. And that error will be 40 times 1 minus 40 divided by our n of 200. So if you calculate whatever is inside, 1 minus 40 is 0. Sorry, not 1 minus 40, this should be 0.40. I wrote it all wrong. So this should be 0.40. I hope you write it, you wrote it right on your side. 1 minus. Give it some time, it will pop up. 1 minus 0.40, I hope you wrote it right. Yes, I did. Yes, so if you do that and 0.40 multiplied by 0.60 divided by 200, multiply by 2.58, the answer you will get on this side will be 0.0894. And we can split it, 0.40 minus 0.0894 and 0.40 plus 0.0894. And if we look at the answer here, it's in 2 decimals. So you will just keep your answers to 2 decimals. The first one, 0.40 minus 0.0894 will give you 0.31. And on this side, 0.40 plus 0.089 will give you 0.409. Which then it means option C is the correct one. Remember those who want to leave? You are more than welcome to leave. I will post the video. And you can go through it at your own times. Next question. And now we move into hypothesis testing. This is a unique line. Now with hypothesis testing, the six steps. So when you get to chapter nine, you can do the cheat sheet for hypothesis testing, for the lean, when the population standard deviation is known, when the population standard deviation is known, and for the proportion, and write all the six steps. Under each six steps, you write the important things that you need to remember under there. How do you find a critical value? How do you calculate your Z value? How do you make use of the decision? Using a critical value or using the P value? Remember when the population standard deviation is known, you can use the critical value and the Z value to make a decision. Or you can use the P value and your P value and the alpha to make a decision. So you need to make sure that you understand those. So if we look at this question, also you need to know how to make decisions based on whether you've been a one-tailed test, a two-tailed test, and when it's a one-tailed test, whether is it a less than or a more than. Because also it's very important, especially when you are doing the P value decision. Based on that, we can look at the hypothesis. It says more than. And since they highlight that more than, then it also tells you what kind of a test are you doing. Like in the exam, you might get more than, you might get less than, or you might get equal, which is a two-tailed test. So with the more than, then you know that it's one-sided. It will help when we look for the critical value because we know that we just use an alpha value and not divide by two. So all these things are very important to remember as well. So if this is your null hypothesis, that says it is more than. What will be your alternative value will state your alternative? This is theory. Remember, your null hypothesis contains an equal sign. And if this is what the researcher wants to prove, and does not have an equal sign, where does it go? It will go into your alternative hypothesis. So then it means in your alternative hypothesis, we will have all the statements that do not have an equal sign. So yeah, they're asking you what will be your alternative hypothesis statement. So since this is a one-sided test, and since it is a one-sided test, therefore it means that statement will go into a null hypothesis. So then the same statement you see there should state the same thing in your alternative. And we're looking for the incorrect answer. So that will be correct. Next step, they're asking you what will be the critical value. Based on the information you are given, which is step number two of the null hypothesis, based on the information you are given, those key words. Is my population standard deviation known? If my population standard deviation is known, therefore it means I must go find Z critical value. And if I'm going to find the Z critical value, this says my alpha is 0,05. So therefore it means I must find my Z alpha. And therefore if I find my Z alpha, because it's a one-sided test, remember that, don't get confused. It's a one-sided test. We're going to find only Z alpha, not Z alpha divided by two. We only find Z alpha divided by two if it's a two-sided test. So it means we're going to find Z of 0,05. Remember I told you to use that table that I gave you. I'm going to go to that table. If you look here on this, it says regardless of what you see here at the top, it gives you your Z of 0,05. Therefore, that will be the answer. If you didn't write this table down when I asked you to, you can go and find your Z alpha of 0,05, which you come here and look for 0,05. So you will come here and say 0,05. If you see those two values, and remember that it's minus 1,4, and those two values at the top will say 4,5. 0,16 and 4,5, which is the same thing as what we found there. So then that will be correct. Then comes the test statistic. Since we're using a Z, therefore our Z test statistic will be the sample mean minus the population mean divided by the standard error, which is the population standard deviation divided by the square root of N. And you just substitute the base. The sample is 1,200 minus your population mean. It's always in the statement. So in your now hypothesis, they will give you this will be your population mean. So it will be 8,000 divided by the standard error, which is 800 divided by the square root of N. Our N is 100. 2.5. And the answer here will be 2.50. 2.5. And yeah, it says it's negative 2.5. Therefore, it means this is the incorrect one. And then that all these are what we just described. So we know that alpha or level of significance is our alpha, which is minus, which is a question. Can you show me how to do this calculation? For the test. What type of data are you using? Are you using case or sharp? Case or if you are using a case or is it the case or with the fraction thingy? Yeah, it to effects not to MS. Do you have this kind of a function on your calculator? You have a fraction five on your calculator. That looks like this laser. It should be a blocky thingy. So you don't see it. So it means you don't have that. Okay, so what you will do. I'm going to do that. You need to remember all these things. So you can say on your calculator, my pen does not want to write anymore. Let me charge it. What you can do on your calculator, say the following. So you can do it step by step or you can do it on your calculator straightforward. It will mean that you say, what is the 800 divided by the square root of 100 and get the answer for that. Then you go to the top. Otherwise, you can use brackets. So I will say right now on your calculator, say 1200 minus 1000 and press equal sign. You need to let me know when you have done it and then say press the division sign. Then divide by then open the bracket. Press the open bracket sign. And then say 800 and say divide by and go find the function that looks like a square root. Is it a button? So if it's just a button, then press that and then press 100 and then close the bracket. OK. And then press equal. Yeah, I think that one of starting with the below ones is much better than this other one. So you can do it this way. Or you can say 800 divided by the square root of 100 and get the answer and then get the answer for the top and then divide each other. So it depends on how you want your calculator. You just need to know how to do it later. OK. This one is better. Right. OK. We'll go to the next question. It's also hypothesis testing. And yeah, it asks two-sided hypothesis testing. So they give you all the other information that you have. The pen is right enough. Two-sided hypothesis testing for the mean with an unknown population standard deviation. So therefore it means they give out that population standard deviation. So yeah, is the other thing you need to also remember. Since they said a two-tail test and I can see that they looking for the p-value and they say the p-value yields 0.03. It means this side and that side of this gives 0.03. It means divide by two. This will be 0.0. So it means this side of the table and this side of the table. The value here was 0.015. That's what they are saying in terms of this information if I look at it because it says a two-sided hypothesis has the p-value of this because we know that for a two-sided it will be two times the p-value that we find on the table. That will give us the actual p-value for a two-sided test. The other thing you need to know because this is more sure if it's a population standard deviation we're using a z-test just because of that. And since we're using a p-value the two questions here it talks about the rejection. Remember the decision when we use the p-value we say if the p-value is less than alpha we reject the null hypothesis. So it means you will need to go and find out if you're going to be rejecting the null hypothesis based on those p-values based on those alpha values. The other thing which is the last question it says the test statistics is less therefore it means they say if this is my z-value if this is my probability of 0.015. This is my probability. It says the probability that z lies between because this lies between the two values and we will because we're using the z-value and go find the probability so we're going to say the z of less than the value we need to find on the table is 0.015 which is what it says. If we need to go find that value on the table we would have used this z-test statistic so we need to go and find whether this 1.88 is at that value. And since this is positive then it means we would have set 1 minus the value that we find on the p-value. So at the moment I'm going to do the three statements and we'll just go and check if one of those is correct. So let's start with the first one. We'll come back to the last one last. If the three statements holds or one of them is incorrect then we don't have to do the last one but I'm just going to show you. So the first one we know that the population standard deviation is given so it's correct. The second one which is B it says the null hypothesis is rejected at that. So we know what our p-value is. Our p-value is 0, 0, 0, 3. That's what we know from the statement that we are given. From that statement we know that our p-value is 0, 0, 3. What is our alpha? Our alpha is 0, 0, 5. So here it says we reject the null hypothesis. So are we rejecting the null hypothesis? Yes we are going to reject because the p-value is less than alpha therefore this is correct. So that will be correct. And the next one it says we're not going to reject the null hypothesis at 0, 0, 1. It means our alpha of 0, 0, 1. Is it less than? No, it is greater than. And when it's greater than we do not reject the null hypothesis. So is this correct? Correct. We are left with D. So with D we know that D will be the one that is not correct. So but how do we make sure that, for example, if they were asking you to find the correct answer and the correct answer is D, you would have found that it will be the one that is incorrect. But how do we find that? So what you can do is go find this T-value, the test statistic value. It is 1,89. 1,89. That's what they gave us. So you go to the table and you will find it on the positive side. Now for a positive side of the value, so we use the positive side of the table because that is the test statistic is your Z-value. Remember that, Neb? The test statistic is your Z-value. So since it will be in the positive side, we are going to say 1 minus the value we find on the positive side of the table. We are going to subtract that. It's 1,89. So we go 1,89 at the end. Take it to the end. So I will have to say 1 minus 0,9706. This answer should give me 0, so this answer should give me 0,015. Is it 0,15? What did we say? It should give me 0,15. So let's see. What does it give me? 1 minus 0.9706 equals 0.0294. So even though it is close to 3, 0.3, you need to be very careful because this set is a two-sided test. When it's a two-sided test, we know that the value we find on the table, we need to multiply it by 2 or we need to add it to each other. It means if this was the P-value, then it means 0.239 or 0.0294. We will have to multiply it by 2 and it would have given us 0,059 which is not the same as 0,030. We just need to know all the basic concepts on how to find the P-values and how to calculate the P-value. This is only because it was a two-sided test. If the question was a one-sided test, then the answer would have been correct for a P-value of 0,015 because for a one-sided test, the value you find on the table would be the value you find on the table and also remember that if your Z-value is positive, you will always need to minus that value you find on the table from 1. So, move on to the next question. Can I ask? Okay. On the two-sided, I only divide the P-value by 2 if it's two-sided. No, don't get confused. When you go find the P-value on the table, you will use your Z-test statistic value. So this is your Z-value and you will say it is 1,8 because we need to use two values. So you will use this to go find the value on the table but because it's positive, you will find minus the value you find on the table. If it was negative, it would have been the value you find on the table. So only for positive, you do this. For a negative, you do that. And also for a negative, only if it's big, I think as well. Sorry, for positive, only if it goes in the positive side of the table, the bigger side of the table, you will need to do that. So the other thing, when you go find the P-value, depending on if it's a two-sided test, remember that you're going to say P-value plus P-value. This is only for the two-sided test or you're going to say two times the P-value. That is for the two-sided test. For a one-sided test, the value you find on the table, it will be your P-value. That's it. No division, no multiplication or nothing. I divided this by two so that I can show you the two sides. You don't have to do that. It was just me trying to explain how did they get 0.03 because it's a two-sided test. Since it's a two-sided test, we know that there are two sides and each side has 0.15, 0.15. We add them together, 0.15, 0.15 plus 0.015. If you add them together, they give you 0.03. That's only what I was trying to demonstrate. This was just to help us answer the last question which is question number D. If we didn't know that it would be 0.015, we would have assumed that this answer is correct. You wouldn't know that it should be 0.015 because you would have said, the answer I find on the table is 0.094, therefore the P-value is 0.03 because you would have rounded it off and it would give you the same answer, which is not correct. Two-sided, this 0.03 is made up of the two sides which they are required. Moving forward. I don't find the P-value on the table. The P-value on the table, we find it by using the Z-value because the test statistic is your Z-value, so you will use your Z-value. We will go to the table. The P-value is this. These are all your P-values. All these values inside the table, we call them probabilities, which are the probability values, P-values, probability values. We will find 1.8 and 9 at the top and this will be your P-value. Because it's in the positive side of the table, we need to say 1 minus the value we find on the table. And that's how you find there. If it's on the negative side of the table, if your P-value, you're going to find it here and your answer is negative. Let's say it was 1.8, so it would be 1.89 and you will see that it would be that value. Only if it's a negative, you come and find the values here. This is mainly because of the structure of the tables. Because if you look at this, it gives the smaller version of the less than table. And if you look at the positive side of the table, it takes also part of the positive side of the table. As you can see that the shading is bigger, so we only interested in that part. And in order for us to get only this part, which is the inverse of this, we just want that smaller portion, not looking for the entire proportion of the area of this table. Okay, so moving forward, which I think will be in almost there. I think this will be 6, we halfway down the line. And now we are in Chi square table. How do I know that we are in the Chi square table? It's because they give me again a contingency table and then they gave you the table. And remember also, I don't know what kind of an assessment you wrote, which tables or what questions did they ask you in terms of your assessment? So you might be getting different assessment in terms of this. So for this one, they're asking for the number of degrees of freedom. Remember the degrees of freedom, the number of rows minus one, and the number of columns minus one. So you count how many rows you have. You have one, two rows, minus one. And how many columns you have? You have two columns. Two. Two minus one. And it should be easy, because it's one times one, which is equals to one. It's number D, C, D. Option D. And this question, they're asking you to find the critical value. So remember, we found our degrees of freedom and we know that our degrees of freedom is one. And our alpha in the system, they gave us its alpha, level of significance of one. So we go find the critical values of zero comma zero one. Remember, this is divided by a hundred, which would be zero comma zero one. And the degrees of freedom of one. So you go to the critical values of T table. Sorry, the critical values of chi, table, T table, and the critical values of chi. This is the table we're looking for. And you come here and you say, we ignore the ones at the top. You say you're looking for alpha of zero comma zero one. And you look here, zero comma zero one, which is the last question. And we look for the degrees of freedom of one, which is the first row. Zero comma zero, six comma six, three five. And we go back. The answer here is option B. So the next one also is the chi square question. And what they did, they give you the hints here. So what they're also trying to do with the exam is to also save you time to do a whole lot of other things. So on this question, they calculated your expected frequencies for you. They are inside the bracket. Remember your expected frequencies? We would have calculated them by saying the row total, multiplied by column total, divided by n. So we would have taken for 29.68, we would have said 56 times 53 divided by 100. It would have given us 29.68. So they already calculated that point. You don't have to go ahead and calculate them again. So what they want you to do is to go calculate your chi square test, which is your sum of your observed minus your expected overall, observed minus expected squared divided by the expected. I don't even have to write the bracket there. So it's your observed minus your expected squared divided by your expected. So you will need to go and calculate it. So our observed is 38 minus 29.68 squared divided by 29.68. It's going to take us forever. 18 times 26. What am I saying? 18 times 18 minus 18 minus 26.32 squared divided by 26.32. So I will assume that you are also calculating. And this will be 15 times 15 minus 23.32 squared divided by 23.32 plus 29 minus 20.68 squared. Divide by 20.68. I must just double check my answers. I'm not going to say anything. I'm giving you time to also do your calculations. And then we can confirm the answer. I'm just going to write them so that you see them on the screen and you can correct them if I am wrong. Are we happy? Yes. Do you agree with the values I have in front of you? Yes. Okay. Since I didn't calculate the final answer, please calculate it and let me know which one. How many to calculate, please? Is this E 11.28? Yeah. 11.28. Okay. And that will be the answer. We are almost done. And this is section, this last study unit, which is your study unit 11, which is regression line. This is your regression line. And this is the slope. Sorry. This is there. The slope equation. So we need to go find the formula that calculate the slope. So they give us the sums sums. So we did this exercises actually as well in class. Remember that? We looked at how do we calculate the slope? So what do you mean the formula? So probably you have written that formula down somewhere where you can always come back and reference it. Remember the formula for the slope is the sum of x, y minus the sum of x times the sum of y divided by n. Everything divided by the sum squared minus the sum of x squared divided by n. X squared minus sum of x squared divided by n. So our sum sum sum of x, y is 11,000. 5.2 minus your sum x is 465 times your sum y is 613 divided by our n. Our sample size is 80. Divide everything by our sum x squared. It's 9455 minus our sum of x 465 squared divided by our n of h. So I'm going to do step by step. So this will be 115.2 minus. This is a monster calculation. 465 times 613 equals divide by 30. I get 950950125 divided by 945 minus and I do the same 465 squared equals divide by 30 equals 7207. That's it. At the top, 11502 minus 9501.5 and that gives me 2000 divided by 9455 minus 7207.5 and that gives me 2247.5. What do you get as an answer? I have done a lot. 0.89. And that gives you 0.89, which is option number 3. So like I said, you will need to write all these formulas down. So you need to make sure that you have that cheat sheet written somewhere for all these formulas. We dedicated two sessions, one Saturday looking at linear regression as well and we looked at the different types of questions. As you can see that this question looks almost exactly like the ones that you got from those assessment A, B and C. So you need to make sure that you go through all those so that you understand how to answer some of these questions as well. And I think this will be our last question. Second last question or last question, I'm not sure. Let's see if we go right to the bottom of this question. This will be our last question. This is also the last regression line. So how do we then answer this question? Anything at the top? Okay, nothing. Suppose you have this relationship where they give you the regression line and they give you R squared. They don't want you to calculate almost anything other than your that you need to know. You need to know how to interpret R squared. You need to know how to calculate or you will have to calculate coefficient of correlation, which is R. And if you have R squared, remember you can take the square root. It will give you R. The square root of R squared will just give you your R. It will answer R and it will answer question number D. The other thing is how you interpret the slope. The intercept, this is the slope. Remember with the slope, everyone unit increase will decrease or increase. The intercept is the average estimate if X is equals to zero. You need to interpret your R squared, which says what percentage of total variation in your Y variable is explained by your X variable. And you need to be able to interpret your R because it's R. Remember, you can get the value of R as your R as negatively correlated, positively correlated. And also the strength of it. Is it the perfect? Is it the strong? Is it the weak relationship? If it's between minus zero, if it's between zero point three and zero, is it a weak relationship? If it's between zero point three and zero point six, is a moderate relationship? And if it is between zero point six and one, it is a strong relationship. And if it is one or minus one, it will be a perfect relationship. And zero will mean no relationship. So you need to know all those things. So based on the information, each one of the following statement is being correct. That's what you're looking for. Number eight, there is no food traffic in the store. That is the food traffic is zero and the store sells online. The sales are estimated at six thousand six hundred and four. So it means if, because this is an excess food traffic. If X is zero, will the store sell average sell at six thousand six hundred and 40 because our sales are in thousands. So we substitute Y is across to six point six four as zero point eight nine and we substitute by zero. And therefore Y is across to six point four six and we multiply this by a thousand and we will find six thousand six hundred and forty. And is this correct? Yes, this will be correct. That's how you will answer the question that we're looking for the incorrect one. The coefficient of correlation is that. So what you do is take the square root of zero comma six zero nine nine. Let me know what you get. What is R? Did you calculate it? R is zero point seven eight zero nine. Which if you round it off it will be zero comma seven eight one zero. Which means this will be the correct one because you get zero comma seven eight zero nine six some number and some other additional number. And if we round it off to three decimal to four decimals. That was that zero comma eight seven eight one zero. That is correct. We move to the next one. Now we were given the R squared. R squared will always be positive because if we calculate the R, we will never know what kind of a sign should be fine in front of that. Whether it's positive or negative because we didn't calculate it. We calculated it based on the R squared B, which is positive. We know what sign should be. We need to also get the sign of the slope. So this is very important. The sign in front of the slope tells us what would have been the sign in front of the R. So the slope is positive. So therefore it means our relationship is also positive. So you get this. It says there is a positive relationship between the food and the sales of the store. And that's what we can look at the sign of the slope, which means that is correct. Now, number D is saying that you need to know how to interpret the slope. You need to know how to interpret the coefficient of determination. Remember the coefficient of determination is equals to zero comma six zero six nine. And the coefficient of determination, when we interpret it, we say what is the percentage of the variation in the Y variable that can be explained in the variation of our X variable. That's how we interpret the coefficient of determination. Based on that information, if we look at our coefficient of determination, it's zero comma six zero one. So we can say if we multiply by 100, it will give us 60. 60. 61%. Let's say it will give us 61%. Or it will give us 60.99%. And we can interpret it by saying 60.99% of the total variation in the store sales is explained by the variation in the food traffic in the store. So if I look at the question D, it says 78%. They're using the value of our coefficient of determination. We should tell us that this is a positive or a because it's between zero point six and one. If we have a strong relationship, then it should have said this is a strong positive relationship between, or there is a strong positive relationship between the sales and the variation. And that is explaining the coefficient of determination, which is zero comma six seven. And this should state 60.99% of the total variation in the sales is explained by the variation in the food traffic in the store. And with that, it concludes today's session. So it took us three hours. In the exam, you will need to finish this by within two hours. To close off the session and to also remind you, remember the exam is two hours. You can start any time of the day between 11 and three o'clock. Make sure that when we take the exam, you make time for break, you go and breathe out. You will have section A and section B or section one and section two. Once you complete with section one, take a minute break or if it doesn't matter how long you take that break. Make sure that you take a break and bring back your thoughts to say I am prepared now to take the second session. Don't start the second session and it becomes so pleasant to say, oh, but I'm panicking. I need to go to the bathroom and all that. Remember, once you start opening the session, the timer will kick off. You will need to accept the terms and t's and c's of the exam as well before you start. You need to approve it so that you know that you are taking the exam. You need to play and then you can start your exam. Please don't start your exam if you see that you have network issues. Don't start it. Wait a bit. Give yourself time. Remember, you can start even from 12, quarter past 12. The lecture also gave you all this information I'm relaying to you. It's part of that EDF document distributed on my life email account. You can start your exam exactly at quarter past 12 or you can start at 11. Make sure that you have strong network connection. You are not going to be disturbed. Make sure that you put away your phone. Make sure that you have your tutorial letter 101 open with the tables on. Make sure that you have your cheat sheet formula document next to you so that you can use it for answering some of the questions. Take your time. Don't hurry. Don't panic. Relax. Take a breathe in between the questions and then continue to pace yourself because you only have an hour one to open that session. Take a break. Please ask for the first session. Whether you start with session two or you start with session one. Make sure that you take at least 30 minutes break or an hour break. It doesn't really matter so that you come back refreshed with the clear mindset that you're going to start looking at your exam. And then open your exam and start again. The exam will be open up until three o'clock. So you have enough time. So you don't have to start immediately at 11. Like I'm going to stress this. You don't have to start immediately at 11 o'clock when everybody comes onto the system because then the system becomes lower. You can give yourself time. You can say I'm going to start at 11 or I'm going to start at 11 or 12. Or at least make sure that by what are past 12, you start at at least one of the exam. And this is only to give those who are having difficulties, challenges and problems. Time to look into the system. Your exam starts at 11 but you have a leading way. So please don't panic when you see that the system is slow. So if you log in at 11 and you see that the system is low. Just say, okay, I'll try in a little bit later. And then 15 minutes after that, you try again. And if it's still slow, try again after 15 minutes. But make sure that by quarter past 12, you have started your exam. Once you have started with your session one, I'm repeating the same thing if you hear me right. Once you have started with your section one exam, the timer will start. You are given an hour to finish. You cannot go back to the question that you didn't answer. You need to make sure that you answer all that. If you will see, you will get a button to say save answers and stop me. You don't have to go ahead and click on save, save, save, save all the time. The questions will always be saved. If the timer runs out and you are still working on your question, do not panic. The system will automatically update your questions or submit your exam for you. Wherever you are on the part of the exam, the questions will automatically be uploaded. Also, your answers will automatically be uploaded onto the system. You do not have to panic. And that's all what I can do. I don't know what I can do for you. So remember also the other thing. On the day of your exam, I will leave the water group open until half past 11. At half past 11, I'm going to switch it off for technical issues. So it means I'm giving you a chance to assist one another or talk to me if you have any difficulties. On the water group, please do not discuss answers. Please do not share if, for example, I forget to switch it off. Please do not discuss answers with one another because every question for every student might be different. You might get a different question to the other students that you are working with or you have on your water group. So every student will get an individualized exam paper. But most of the questions will be exactly the same at different questions. So sometimes the question might ask one student for incorrect answer. Sometimes one student might get the correct answer. Sometimes it might change the balance. Instead of less than 0.8, they might give you more than 0.8. Instead of more than 0.64, they might give you. So you will get different exam papers. Please, please, please stay away from the water group or what you call the other social media thing. The other type of similar chat room that looks like water. It will just distract you. You have everything. It's easy. You can get 100%. It's easy. We have done everything. We have gone through the assessment one that I gave you, the online assessment chapter 1, chapter 6, and chapter 1. You can see that similar questions are asked. We have gone through that assessment. We have gone through assessment A and B of linear regression. You have assessment 1-7 of the other thing and with ANTAS as well, because I gave you the ANTAS for that assessment. Make sure that you go through practice, practice, practice, practice. It's easy to get 100% if not in the exam because if you know everything, there's nothing wrong with you getting 100%. There's nothing that can stop you because we have practiced everything. Even what we did today is not something that is true. We have done it in class. We've worked through some of the examples we used in class look exactly the same as what we have done today. You have everything you need to write this exam. Do not panic. Take a breather. Make yourself rainbow tea. Don't make coffee. Make sure that your mind, your brain, your soul is ready for the exam. Don't panic. Don't look at what people are saying on the WhatsApp and they're just going to make your life miserable. Just concentrate on your own face. Your own exam and everything will go right. Make sure that you write that cheat sheet formula sheet that I spoke about. Make him make like small things that you still unsure about it. Write it. I'll say remember to do one, two, three, four. Remember to one, two, three, when you answer questions like this, this is the formula. This is how we change the formula. All those things. Make it easy for yourself and pace yourself with all that. I wish you all the best with the exam. Please don't leave the WhatsApp group. You can leave the WhatsApp group after you have received your exam back and then so that we can check about. So what I would like to do as well after your exam, we can I will open the the WhatsApp group and then we can check. We can reflect on how the exam was. You can talk about your experiences, how you enjoyed the exam and how you're looking forward to your results and so forth. And you can query anything you can ask any questions there and you can talk. And then we can also use the WhatsApp group again after the exam results about to just break out ourselves. How well we did or not how well we did or whether we wrote the exam or not and encourage one another. Don't worry. Other than that, from me to you, thank you for being part of this sessions and thank you. Thank you. Thank you. Thank you. Thank you for participating and always watching the videos and even though you didn't talk to me on my UNISA. So thank you very much for participating and downloading the material and also taking part in watching the videos that we both co-created and all the best. Thank you. Enjoy the rest of your Saturday. Thank you. Thank you so much for your help. Thank you so much. Thank you. Thank you ma'am. Appreciate it.