# Question

A survey research group conducts regular studies of households through mail questionnaires and is concerned about the factors influencing the response rate. In an experiment, 30 sets of questionnaires were mailed to potential respondents. The regression model fitted to the resulting data set was as follows:

Y = β0 + β1X1 + β2X2 + ε

where

Y = percentage of responses received

X1 = number of questions asked

X2 = length of questionnaire in number of words

Part of the SAS computer output from the estimate regression is shown next.

R@Square = 0.637

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 1% significance level, the null hypothesi that, taken together, the two independent variables do not linearly influence the response rate.

d. Find and interpret a 99% confidence interval for β1.

e. Test the null hypothesis

H0: β2 = 0

against the alternative

H0: β2 < 0

and interpret your findings.

Y = β0 + β1X1 + β2X2 + ε

where

Y = percentage of responses received

X1 = number of questions asked

X2 = length of questionnaire in number of words

Part of the SAS computer output from the estimate regression is shown next.

R@Square = 0.637

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 1% significance level, the null hypothesi that, taken together, the two independent variables do not linearly influence the response rate.

d. Find and interpret a 99% confidence interval for β1.

e. Test the null hypothesis

H0: β2 = 0

against the alternative

H0: β2 < 0

and interpret your findings.

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