Given the linear regression equation x 3 16 5 4 0x 1 9 2x 4 1 1x 7 (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 x 1 10, x 4 1, and x 7 2, what is the predicted value for x 3 (d) Explain how each coefficient can be thought of as a slope Suppose x 1 and x 7 were held as fixed but arbitrary values If x 4 increased by 1 unit, what would we expect the corresponding change in x 3 to be If x 4 increased by 3 units, what would be the corresponding expected change in x 3 If x 4 decreased by 2 units, what would we expect for the corresponding change in x 3 (e) Suppose that n 15 data points were used to construct the given regression equation and that the standard error for the coefficient of x 4 is 0 921 Construct a 90 confidence interval for the coefficient of x 4 (f) Using the information of part (e) and level of significance 1 , test the claim that the coefficient of x 4 is different from zero Explain how the conclusion has a bearing on the regression equation

Question: Given the linear regression equation x 3 = 16.5+ 4.0x 1 +9.2x 4 1.1x 7 (a) Which variable is the response variable? Which variables are

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.

(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.

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