Given the linear regression equation

x₁ = 1.6 + 3.5x₂ – 7.9x₃ + 2.0x₄

(a) Which variable is the response variable? Which variables are the explanatory variables?

(b) Which number is the constant term? List the coef­ficients with their corresponding explanatory variables.

(c) If x₂ = 2, x₃ = 1, and x₄ = 5, what is the predicted value for x₁?

(d) Explain how each coef­ficient can be thought of as a “slope” under certain conditions. Suppose x₃ and x₄ were held at ­xed but arbitrary values and x₂ was increased by 1 unit. What would be the corresponding change in x₁?

Suppose x₂ increased by 2 units. What would be the expected change in x₁? Suppose x₂ decreased by 4 units. What would be the expected change in x₁?

(e) Suppose that n = 12 data points were used to construct the given regression equation and that the standard error for the coef­ficient of x₂ is 0.419.

Construct a 90% confidence interval for the coefficient of x₂.

(f) Using the information of part (e) and level of signifi­cance 5%, test the claim that the coeffi­cient of x₂ is different from zero. Explain how the conclusion of this test would affect the regression equation.