# A survey research group conducts regular studies of households through mail questionnaires and is concerned about the

## 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 = Î²0 + Î²1X1 + Î²2X2 + Îµ
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 Î²1.
e. Test the null hypothesis
H0: Î²2 = 0
against the alternative
H0: Î²2 and interpret your findings.

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