Given the linear regression equation

x₃ = –16.5+ 4.0x₁ +9.2x₄ –1.1x₇

(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 x₁ = 10, x₄ = ­1, and x₇ = 2, what is the predicted value for x₃?

(d) Explain how each coeffi­cient can be thought of as a “slope.” Suppose x₁ and x₇ were held as fi­xed but arbitrary values. If x₄ increased by 1 unit, what would we expect the corresponding change in x₃ to be? If x₄ increased by 3 units, what would be the corresponding expected change in x₃? If x₄ decreased by 2 units, what would we expect for the corresponding change in x₃?

(e) Suppose that n = 15 data points were used to construct the given regression equation and that the standard error for the coef­ficient of x₄ is 0.921.

Construct a 90% confidence interval for the coefficient of x₄.

(f) Using the information of part (e) and level of signifi­cance 1%, test the claim that the coef­ficient of x₄ is different from zero. Explain how the conclusion has a bearing on the regression equation.