Question

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

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

Range of independent variables

The range of x₁, x₂, and x₃ is 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 x_1,x₂ and x₃are well within the range of values. While when x₁ = 60, x₂ = 0.4, and x₃ = 900, x₁and x₂ are out of the range and x₃ is within the range.

Conclusion

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