 Hello, this is a video about linear regression predicting values. Suppose you run a correlation and find the correlation coefficient is 0.246 and the regression equation is y hat equals 2.6x plus 8.42. Also, x bar, the average of the x values, is 5.3 and y bar, the average of the y values, is 22.4. If the critical value is 0.497, use the appropriate method to predict the y value when x is 3.9. All right. So naturally, you may want to take x and plug in 3.9 and for it into the linear regression equation, which probably 75% of the time that will be accurate. However, in order to use the linear regression equation, in order to plug values into it to make predictions, you must show that there is linear correlation first. You must show that this equation holds true. So what we have to do is we have to compare the correlation coefficient r to the positive critical value. In this case, correlation coefficient is 0.246 and the critical value is 0.497. So let's compare 0.246 to 0.497. It is clearly less than, the correlation coefficient is clearly less than the critical value. So that means I, in my hypothesis, I would fail to re-inject H naught, but the important thing is that means that there is not linear correlation. So guess what we can't use in this example? We cannot use this linear regression equation. So you might be thinking, well, how do we predict the y value when x is 3.9? Well, anytime you can't use the linear regression equation, meaning there is not linear correlation, you will use y bar or the average of the y values as the best prediction. It might seem a little weird, but this is the protocol. This is what you should do. So the best estimate is 22.4. That is your y bar. That's why they gave it to you in the question. So 22.4 is the predicted y value when x is 3.9. That's because we cannot use the linear regression equation because we showed that there is not linear correlation using a correlation coefficient and critical value comparison. Keep these in mind. All right, so that's all I have for you for now. Thank you for watching.