Statistical Literacy Given the linear regression equation x3 5216.5 1 4.0x1 1 9.2x4 21.1x7

(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 510, x4 521, and x7 5 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 515 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.

AppendixLO1