1. Residuals (resids)

2. 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 𝑛−2

3. 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

4. Please verify your calculations

5. Calculate the regression line using the previous data
𝑏=𝑟 𝑠 𝑦 𝑠 𝑥 = .92∗ =2.8 (or the slope is 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 = 𝑥

6. Calculate the resids for the previous
Data and the regression equation 𝑦 = 𝑥

8. 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!