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Q11-15E

Expert-verified
Found in: Page 653

### Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593

# 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: $\stackrel{\mathbf{^}}{\mathbf{\text{y}}}\mathbf{\text{= 14 - 2.5x.}}$c. Show that SSE is larger for the line in part b than for the least-squares line.

1. Fig. 1 Table.
2. Fig. 2 Table, Fig. 3 Scatterplot diagram.
3. SSE is smaller than the least square.
See the 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 $\stackrel{^}{\text{y}}$ from y, the residual is the vertical distance between the observed and anticipated points.

## Step 2: Complete the table

From exercise 11.14, we have

$\stackrel{\mathbf{^}}{\mathbf{\text{y}}}{\mathbf{\text{=1.78 +}}}\mathbf{\left(}\mathbf{-}\mathbf{\text{0.77}}\mathbf{\right)}{\mathbf{\text{x}}}$

## Step 3: Draw a scatterplot of the data and plot the least-squares line. On the same graph, draw the following line

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

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

## Step 4: Show that SSE is larger for the line in part b than for the least-squares line

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

108 < 153.6.39

Therefore, SSE is smaller than the least square.

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