Suppose you have developed a regression model to

Chapter 12, Problem 132SE

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QUESTION:

Suppose you have developed a regression model to explain the relationship between y and \(x_1\), \(x_2\), and \(x_3\). The ranges of the variables you observed were as follows: \(10\ \leq\ y\ \leq\ 100,\ 5\ \leq\ x_1\ \leq\ 55,\ .5\ \leq\ x_2\ \leq\ 1,\ \text{and}\ 1,000\ \leq\ x_3\ \leq\ 2,000\). Will The error of prediction be smaller when you use the least squares equation to predict y when \(x_1\) = 30, \(x_2\) = .6,and \(x_3\) = 1,300, or when \(x_1\) = 60, \(x_2\) = .4, and \(x_3\) = 900?Why?

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QUESTION:

Suppose you have developed a regression model to explain the relationship between y and \(x_1\), \(x_2\), and \(x_3\). The ranges of the variables you observed were as follows: \(10\ \leq\ y\ \leq\ 100,\ 5\ \leq\ x_1\ \leq\ 55,\ .5\ \leq\ x_2\ \leq\ 1,\ \text{and}\ 1,000\ \leq\ x_3\ \leq\ 2,000\). Will The error of prediction be smaller when you use the least squares equation to predict y when \(x_1\) = 30, \(x_2\) = .6,and \(x_3\) = 1,300, or when \(x_1\) = 60, \(x_2\) = .4, and \(x_3\) = 900?Why?

ANSWER:

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Here we have the following ranges for the given response and explanatory variables.

 

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