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

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Random Sample

A recent article in Buisness Week listed the best small companies. We are interested in the current results of the companies sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

Company Sales Earnings
($ millions) ($ earnings)

Papa John's International 89.2 4.9

Applied Innovation 18.6 4.4

Integracare 18.2 1.3

Wall Data 71.7 8.0

Davidson Associates 58.6 6.6

Chico's Fas 46.8 4.1

Company Sales Earnings
($ millions) ($ millions)

Checkmate Electronics 17.5 2.6

Royal Grip 11.9 1.7

M-Wave 19.6 3.5

Serving-N-Slide 51.2 8.2

Daig 28.6 6.0

Cobra Golf 69.2 12.8

Let sales be the independent variable and earnings be the dependent variable.

A. Draw a scatter diagragm.

B. Compute the co-efficient of correlation.

C. Compute the co-efficient of determination.

D. Interpret your findings in part B and C.

E. Determine the regression equation.

F. for a small company with 50.0 million in sales, estimate the earnings.

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