 Hello, this is a video about linear regression predicting values. Suppose you run a correlation and find the correlation coefficient is 0.677 and the regression equation is y hat equals 6.1x minus 25.93. Also x bar equals 7.3 and y bar equals 18.8. If the critical value is 0.396, use the appropriate method to predict the y value when x is 10.1. Now you might want to take 10.1 and plug it in for x in the linear regression equation. However, you cannot plug anything or use the regression equation to make predictions until you show that there is linear correlation. So to show there is linear correlation, we need to compare the correlation coefficient with the positive critical value. In this example, the correlation coefficient is 0.677 and the critical value is 0.396. So let's compare 0.677 to 0.396. So the correlation coefficient looks like it is greater than the critical value, which puts us in this top portion here. So we reject H naught and our hypothesis for linear correlation, but that's really not too important on this example. What's important is the fact that when this happens, there is linear correlation. That means you can use the regression equation to make predictions. So that means I'm going to let x equal 10.1. In the equation, y hat equals 6.1x minus 25.93. So my predicted y value, y hat is 6.1 times 10.1 minus 25.93. Use your calculator to compute this and it turns out that you'll end up getting 35.68 is the predicted y value when x is equal to 10.1. So this is an example of making predictions and we can use the regression equation because we showed that there is linear correlation. When there is not linear correlation, you would have to use y bar, the average of the y values as your answer for your predicted y value. So that's all I have for you today. Thanks for watching.