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Interpretations of Regression Coefficients

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1. Thirty-two data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is

a. The equation of the sample regression line is: = __________________________.
b. There are ______ degrees of freedom for the t-test. At the 5% level of significance, the critical t-value for the test is ______________.
c. At the 5% level of significance, __________ (is, not) significant, and ________ (is, is not) significant.
d. At the 2% level of significance, the critical t-value for a t-test is ___________. At the 2% level of significance, _________ (is, is not) significant, and _________ (is, is not) significant.
e. The p-value for indicates that the exact level of significance is ______ percent, which is the probability of _________________________________________.
f. At the 5% level of significance, the critical value of the F-statistic is _______. The model as a whole ___________ (is, is not) significant at the 5% level.
g. If X equals 240, the fitted (or predicted) value of Y is ____________________________.
h. The percentage of the total variation in Y that is NOT explained by the regression is ________.

2. Schools with larger enrollments might have more resources, making their students better prepared and more valuable to employers and, subsequently, commanding a higher salary. Of course, smaller schools may give students more personal attention, which develops better skills and could yield a higher salary for smaller schools. Studying the relationship between mean base salary and enrollment might help us understand this relationship better. (Use bschools2002.xls)

a. Uses excel to perform a regression of mean base salary vs. enrollment. Write the estimated regression equation.
b. Use your regression equation to estimate the mean base salary for a school that enrolls 800 students.
c. Use your regression equation to estimate the mean base salary for a school that enrolls 1,800 students.
d. Interpret the p-value of the independent variable.

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Solution Summary

Step by step method for regression coefficient and interpretations are given in the answer.

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