Statistical Literacy Given the linear regression equation x1 51.6 1 3.5x2 2 7.9x3 1 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 5 2, x3 51, and x4 5 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 fixed 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 512 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.

AppendixLO1