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Chapter 11: Q11-15E (page 653)

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:

y^= 14 - 2.5x.

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

Short Answer

Expert verified

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

01

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 subtractingy^from y, the residual is the vertical distance between the observed and anticipated points.

02

Complete the table

From exercise 11.14, we have

y^=1.78 +(−0.77)x

03

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

y^= 14−2.5x.

By putting the x value in the above equation, we get y^:

04

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

SSE of y^= 14−2.5x is smaller than the least square, i.e.

108 < 153.6.39

Therefore, SSE is smaller than the least square.

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Most popular questions from this chapter

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