 N minus one so this is going to be a one let's put an underline font group and underline and this will be in Minus one without the colon. I'm going to pull this to the outside 310 minus one Hold on a second equals three ten minus the one and so let's indent this home tab alignment indent and Then indent and then this will be the R or the Correlation and so this is going to be of course Division now because now we have this whole top bit and now we have this this bottom part the numerator and the denominator So this is going to be equal to the 309 Divided by the 309 which comes out to one if we look at the decimals home tab number It should be exactly one. So just a quick recap here We basically to reformat this formula. We're summing up the z-scores We took the z-scores of x the z-scores of y for each data point here We multiplied them together Then we summed up all of the multiplied together z-scores giving us in essence the numerator Then we got to the denominator Which is in or the count of the data which we did with this count formula You could have counted any of these columns. We're not summing up the data here We're just counting how many rows there are and you'll recall when we first spit out the data set we made 310 as our Jit random number generator That's how many numbers we made and then we subtract one n minus one that gives us the 309 And if we divide the numerator by the denominator we get to one. All right, let's underline this now There's some neat stuff in Excel that can kind of analyze this data faster for us It's often useful to do this kind of process because you can then see the z-scores and the relationships With the z-scores, but let's try it this way now I'm going to make a skinny D over here skinny ad and then let's let's say this is going to be my my Automatic calculation, so I'm going to go to the data tab We're going to go to this analysis again and go into the data analysis We showed how to turn this on in the prior presentation this time. I want to go to the correlation That's what we're looking at correlation here, right? Let's go into that in the analysis I'm going to find my data set now. I have to have my data next to each other So I'm going to select this item here and so I'm going to pick my data I have to I have to pick my data so it's next to each other here So I'll start with the inches and the feet of our original data set that we created control shift down and then control Backspace and there's our data sets. I'm gonna say okay, and then columns. I want to in columns And I did include the labels. That's what this is doing here So I included the labels so I want to make sure to check that off and then the output range I'm going to change this to an output range and the place I want to put it is I'll just say right there in a E1 let's say okay, and then it spits this little worksheet out for us nice and neatly so I can then Highlight this I like to make this my format header format again font group black white We can round we can round this home tab Alignment let's wrap this and so there we have it and so now this this shows us nice and quickly The the Correlation right so here's that what we're really looking at so this is this box what this is looking at here This number one here is looking at the feet and the inches correlation So that's the one that we're kind of looking at and it's got a one and that's a perfect correlation So when we're looking at these correlations the one Would be the the perfectly correlated. That's why we have a Straight line now just to just to note this kind of data generator also Let's just play with another one that we that we might commonly use that will spit out some of the calculations We've looked at in the past which would be into the data Let's go into the analysis and data analysis and this time. Let's look at the Descriptive statistics one just to get familiar with that so I'm going to put the input range I'm going to go back on over again. I'm looking at the two Original columns that we had so I'll pick up these two columns control shift down control backspace and then grouped by column I'm going to include the labels again because we had the labels up top and then the output range I want to put it in is going to be let's put it over here now We'll put it right there boom and then down here. I want to have the summary statistics That's what I'm really looking for later on. You might have these confidence level for the mean We might talk about that later 95. We'll keep that as the confident level We'll talk more about that possibly in a future presentation, but we'll say okay and Then it gives us our data so this should give us some of that familiar data that we've we've been working with and And you could see you know the mean The mean that the standard error which you know might not always be applicable depending on the type of data the media and the mode The standard deviation the sample variance the kurtosis we might