Statistics for Business and Economics (13th Edition)
Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Chapter 12, Problem 12.134LM

Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x1 ≤ 55, .5 ≤ x2 ≤ 1, and 1,000 ≤ x3 ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x1 = 30, x2 = .6, and x3 = 1,300, or when x1 = 60, x2 = .4, and x3 = 900? Why?

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To determine
For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2andx3 . The ranges for each of the independent variables are 5x155 , 0.5x21 and 1,000x32,000 . The response variable in the regression model is y, the range of y is 10y100 . The two set of values mentioned are x1=30,x2=0.6andx3=1,300 , x1=60,x2=0.4andx3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2andx3 . Consider the values x1=60,x2=0.4andx3=900 , it can be observed that all the values of the independent variables x1,x2andx3 are not within the range of the variables; this implies that the values x1=60,x2=0.4andx3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6andx3=1,300 , it can be observed that all the values of the independent variables x1,x2andx3 are within the range of the variables this implies that the values x1=30,x2=0.6andx3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

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Chapter 12 Solutions

Statistics for Business and Economics (13th Edition)

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