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Chapter 12: Q134SE (page 807)

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, 0.5 ≤ 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 = 0.6, and x3 = 1,300, or when x1 = 60, x2 = 0.4, and x3 = 900? Why?

Short Answer

Expert verified

Therefore, when predicting y values, the error of prediction will be smaller when x1 = 30, x2 = 0.6, and x3 = 1300 since the values of independent variables are well within the range described in the question.

Step by step solution

01

Range of independent variables

The range of x1, x2, and x3is given as 5 ≤ x1≤ 55, 0.5 ≤ x2≤ 1, and 1,000 ≤ x3≤ 2,000. When x1= 30, x2= 0.6, and x3= 1300, all the variables x1,x2and x3are well within the range of values. While when x1= 60, x2= 0.4, and x3= 900, x1and x2are out of the range and x3is within the range.

02

Conclusion

Therefore, when predicting y values, the error of prediction will be smaller when x1 = 30, x2 = 0.6, and x3 = 1300.

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Most popular questions from this chapter

Question: Suppose you fit the first-order multiple regression model y=β0+β1x1+β2x2+ε to n=25 data points and obtain the prediction equationy^=6.4+3.1x1+0.92x2 . The estimated standard deviations of the sampling distributions of β1 and β2are 2.3 and .27, respectively

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