Given the linear regression equation x 1 1 6 3 5x 2 7 9x 3 2 0x 4 (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 2 2, x 3 1, and x 4 5, what is the predicted value for x 1 (d) Explain how each coefficient can be thought of as a slope under certain conditions Suppose x 3 and x 4 were held at xed but arbitrary values and x 2 was increased by 1 unit What would be the corresponding change in x 1 Suppose x 2 increased by 2 units What would be the expected change in x 1 Suppose x 2 decreased by 4 units What would be the expected change in x 1 (e) Suppose that n 12 data points were used to construct the given regression equation and that the standard error for the coefficient of x 2 is 0 419 Construct a 90 confidence interval for the coefficient of x 2 (f) Using the information of part (e) and level of significance 5 , test the claim that the coefficient of x 2 is different from zero Explain how the conclusion of this test would affect the regression equation

Question: Given the linear regression equation x 1 = 1.6 + 3.5x 2 7.9x 3 + 2.0x 4 (a) Which variable is the response variable?

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.

(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 x₂was 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.

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