 Hello, this is a video about linear regression, calculating the correlation coefficient. Based on the data shown, calculate the correlation coefficient. At the 0.05 significance level, does the data show significant correlation? So to find our correlation coefficient, we need to use Google Sheets. So in Google Sheets, you are going to go to the Regression tab. Once you're in the Regression tab, you'll enter your first column of data in column A, second column of data in column B. Be sure to start typing in row two. So for my x values, I have three, four, five, and you just continue typing it. Be sure to clear out any data that does not belong, and then we'll type in our data for column B for the y values. Now it might be a little bit easier if you were to take the data and the question and directly and copy and paste it into the Google Sheets. If it doesn't copy and paste over nicely, you can open up the Excel document and copy and paste the data in there, and then move it over to the Google Sheets document by copying column by column. So you can copy from Excel and it does work for you. So that's the best way to get around if you can't copy directly from the question in the Google Sheets. All right, so now let it calculate a little bit. It looks like it doesn't take too long for it to calculate. But over here in cell E2, that is actually going to be your correlation coefficient, which we call R. Correlation coefficient is R. All right, so that being said, it's about 0.965, 0.965, R equals 0.965. And the second part of the question, at the 0.05 significance level, does the data show a significant correlation? Any time we run a test for correlation, there's always two hypotheses. And the two hypotheses are always the same from one example to the other. The null hypothesis is always going to be rho is equal to 0. The alternative hypothesis is always saying rho is not equal to 0. And then this equality is still going with the null hypothesis. What rho is is kind of like the population correlation coefficient, whereas R is the sample correlation coefficient. What does it mean when rho equals to 0? Well, this just means that there is no correlation. And when rho is not equal to 0, there is correlation of some sort. So to perform a hypothesis test, I have an alpha value of 0.05. This is alpha. And I need to compare this to a p-value, compare this to the p-value. So we can pull the p-value from the same location in Google Sheets. As you can see, it's very low. It's pretty much 0. The p-value is pretty much 0. So p-value is 0. This is definitely less than 0.05. Any time the p-value is less than alpha, we reject the null hypothesis. So we reject the null hypothesis. Since we're able to reject the fact that there is no correlation, that means there is evidence to support correlation. So there is significant evidence to show that correlation does exist. Thank you for watching.