these are the values in ariels data set. (1, 67), (3, 88), (5, 97), (6, 101), (8, 115) ariel determines the…

Explanation:

Step1: Recall residual formula

Residual $e = y-\hat{y}$, where $y$ is the actual - value and $\hat{y}$ is the predicted value.

Step2: Calculate predicted values for each $x$ - value

For $(x = 1)$: $\hat{y}=6.5\times1 + 63.8=6.5+63.8 = 70.3$. Residual $e_1=67 - 70.3=- 3.3\approx - 3$. For $(x = 3)$: $\hat{y}=6.5\times3+63.8 = 19.5+63.8=83.3$. Residual $e_2=88 - 83.3 = 4.7\approx5$. For $(x = 5)$: $\hat{y}=6.5\times5+63.8=32.5 + 63.8 = 96.3$. Residual $e_3=97 - 96.3 = 0.7\approx1$. For $(x = 6)$: $\hat{y}=6.5\times6+63.8=39+63.8 = 102.8$. Residual $e_4=101 - 102.8=-1.8\approx - 2$. For $(x = 8)$: $\hat{y}=6.5\times8+63.8=52+63.8 = 115.8$. Residual $e_5=115 - 115.8=-0.8\approx - 1$.

Step3: Plot the points

The points to plot on the residual - plot are $(1,-3),(3,5),(5,1),(6, - 2),(8,-1)$.

Answer:

The points to be plotted on the residual plot are $(1,-3),(3,5),(5,1),(6, - 2),(8,-1)$.