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Regression Analysis - Random Sampling

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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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Solution Summary

A regression analysis is shown by random sampling of the data. The correlations between the data can be seen in the analysis as well as the scatter diagram provided in the solution. Interpretations of the results can also be found in the solution.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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