 Hello. This is a video about linear regression making predictions. Monthly high temperatures in a certain location have been tracked for several months. Let X represent the month and Y the high temperature in degrees Fahrenheit. Based on the data shown at the 0.05 significance level, is the correlation significant? What is the best prediction of the high temperature in month 16? So what we're going to do here is we need to run a test to see if linear correlation does hold. And we can do this by using Google Sheets, putting our data into the regression tab, extracting a p-value and comparing it to alpha. If the p-value is less than alpha, there is linear correlation. If the p-value is greater than alpha, there is not linear correlation. If there's linear correlation, then we can use the linear regression equation that we get from Google Sheets to make predictions. If there's not linear correlation, then the best prediction is the average of the Y values. So let's go ahead and put this data in Google Sheets. I went ahead and I took the data from the example and put it into an Excel spreadsheet. Then I'm going to copy over the data column by column. So we're going to go to the Google Sheets spreadsheet to the regression tab, paste the data into cell A2. I'm going to go ahead and clear out any data that's in column Y. And we'll go back to our Excel spreadsheet, copy over our Y data, put that in Google Sheets. So all of my data is now in Google Sheets. And the only thing you need out of here for now would be the p-value, .0009. So we take our p-value, which is equal to .0009, and we compare it to alpha. So in this case, our level of significance is .05, that's alpha. Our p-value is clearly less than alpha. So since we're below alpha or less than alpha, there is linear correlation. There is linear correlation. So now I need to write a linear regression equation, which I can pull from Google Sheets as well. A and B are the two numbers you need for the equation. A is 15.43. B is about 1.97. So the equation is going to be, we'll say Y, or you can use Y hat because this is an equation that's used for predictions. Hats mean we're predicting. Y hat equals 1.97x plus 15.43. So now that we have this linear regression equation, since there is linear correlation, we can just plug in 16. So Y hat equals 1.97x16 plus 15.43. Use your calculator to calculate this value, and you're going to get about 46.95 degrees Fahrenheit. That is the best prediction. Well, let's try another data set. So let's try another data set and see if we can make predictions with it using the regression equation. So based on the data shown at the 0.05 significance level is the correlation significant. What is the best prediction when X equals 15? So once again, I can take this data and I can put it in the Google Sheets. I already have it in an Excel spreadsheet. I copied it over from the question. So I'm going to copy over column by column into the Google Sheets spreadsheet. Go ahead and clear out any old data you have. Paste your X's. Let's copy over the Y values. Let Google Sheets do its calculating for you. And it looks like this time we have a p-value of about 0.0981. So that's p-value is 0.0981. We have to compare it to alpha. We have to compare it to our significance level. Notice the p-value of 0.0981 is certainly greater than alpha. This means that there is not linear correlation. So there is not linear correlation in this case, which means to make a prediction, I cannot use the linear regression equation. Instead, the best prediction is the mean of the Y values. That's the protocol that's done here. We use the mean of the Y values. And you can either add up all the Y values and divide by how many you have, or you can utilize Google Sheets. So you can actually copy your Y value from your spreadsheet document Excel. You can go to Google Sheets in the one variable stats tab. You can go ahead and paste your data into column A. So I'm pasting the Y values in column A. And I'm only concerned with the mean, the average of the Y values here. The average is about 19.64. That's 19.64. So 19.64 is the best prediction. The mean of the Y values. Alright, so that is how you make predictions using linear regression for the p-value alpha comparison method. Thank you for watching.