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Statistics For Business And Economics
Found in: Page 653
Statistics For Business And Economics

Statistics For Business And Economics

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

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Short Answer

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.


  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-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 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

y^=1.78 +(0.77)x

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

y^= 142.5x.

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

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

SSE of y^= 142.5x is smaller than the least square, i.e.

108 < 153.6.39

Therefore, SSE is smaller than the least square.

Most popular questions for Math Textbooks

Is honey a cough remedy? Does a teaspoon of honey before bed really calm a child’s cough? To test the folk remedy, pediatric researchers carried out a designed study conducted over two nights (Archives of Pediatrics and Adolescent Medicine, December 2007). A sample of 105 children who were ill with an upper respiratory tract infection and their parents participated in the study. On the first night, the parents rated their children’s cough symptoms on a scale from 0 (no problems at all) to 6 (extremely severe) in five different areas. The total symptoms score (ranging from 0 to 30 points) was the variable of interest for the 105 patients. On the second night, the parents were instructed to give their sick child a dosage of liquid “medicine” prior to bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM)—an over-the-counter cough medicine—while others were given a similar dose of honey. Also, a third group of parents (the control group) gave their sick children no dosage at all. Again, the parents rated their children’s cough symptoms, and the improvement in total cough symptoms score was determined for each child. The data (improvement scores) for the study are shown in the table below, followed (in the next column) by a Minitab dot plot of the data. Notice that the green dots represent the children who received a dose of honey, the red dots represent those who got the DM dosage, and the black dots represent the children in the control group. What conclusions can pediatric researchers draw from the graph? Do you agree with the statement (extracted from the article), “Honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection”?


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