Question

Refer to Exercise 11.14. After the least-squares line has been obtained, the table below (which is similar to Table 11.2) can be used for (1) comparing the observed and the predicted values of y and (2) computing SSE.

a. Complete the table.

b. Plot the least-squares line on a scatterplot of the data. Plot the following line on the same graph:

$\widehat{\mathbf{\text{y}}}\mathbf{\text{= 14 - 2.5x.}}$

c. Show that SSE is larger for the line in part b than for the least-squares line.

Short answer

Answer

1. Fig. 1 Table.
2. Fig. 2 Table, Fig. 3 Scatterplot diagram.
3. SSE is smaller than the least square.

Step-by-step solution

Step-by-Step Solution Step 1: Introduction

The line that minimizes the squared sum of residuals is known as the Least Squares Regression Line. By subtracting$\widehat{\text{y}}$from y, the residual is the vertical distance between the observed and anticipated points.

Complete the table

From exercise 11.14, we have

$\widehat{\mathbf{\text{y}}}\mathbf{\text{=1.78 +}}\mathbf{(}\mathbf{-}\mathbf{\text{0.77}}\mathbf{)}\mathbf{\text{x}}$

Draw a scatterplot of the data and plot the least-squares line. On the same graph, draw the following line

$\widehat{\mathbf{\text{y}}}\mathbf{\text{= 14}}\mathbf{-}\mathbf{\text{2.5x.}}$

By putting the x value in the above equation, we get $\widehat{\text{y}}:$

Show that SSE is larger for the line in part b than for the least-squares line

SSE of $\widehat{\mathbf{\text{y}}}\mathbf{\text{= 14}}\mathbf{-}\mathbf{\text{2.5x}}$ is smaller than the least square, i.e.

108 < 153.6.39

Therefore, SSE is smaller than the least square.