Residuals (resids)

Residuals are.. A residual is just the difference of the actual value of the response (dependent variable) minus the expected value or the y-hat ( 𝑦 ) value. A plot of the residuals from a strong relationship should look totally random. We can calculate the standard deviation of the residuals using the formula 𝑠 𝑟𝑒𝑠𝑖𝑑𝑠 = 𝑦− 𝑦 2 𝑛−2

For homework, you should have calculated “r” (correlation coefficient) for the following data x y 1 10 2 8 3 12 4 16 5 20

Please verify your calculations

Calculate the regression line using the previous data 𝑏=𝑟 𝑠 𝑦 𝑠 𝑥 = .92∗ 4.817 1.58 =2.8 (or the slope is 2.8. Note, .92 is a strong r). 𝑎 𝑦_𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝑦 −𝑏 𝑥 =13.2−2.8∗3=4.8 So our regression line is 𝑦 =4.8+2.8𝑥

Calculate the resids for the previous Data and the regression equation 𝑦 =4.8+2.8𝑥

analysis The residual plot is not as good as we would like to see. Ideally, The pattern would be more random (as if this were a target shot with a shot gun). With this plot, there is more positive (4.8 more), residual value then negative. We will look at other ways to find a better fit shortly!