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Regression Analysis

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See the attached file.

Nine different students were given version A of a test to determine their knowledge of statistical concepts. The students then took a course in statistical concepts. At the end of the course the students took version B of the same test. You are asked to determine if the course was effective in improving their scores.

(the scores and chart are in the attachment)

A. Construct a scatter plot for the test data.
B. Find the correlation coefficient r and the coefficient of determination.
C. Interpret the coefficient of determination.
D. Is the correlation coefficient significant at the 0.05 level of significance?
E. How would you describe the correlation between the two test scores?
F. Use the sample test data to find the equation of the regression line that would be used to predict a score(on B) after taking the course using the score (A) on the test given before the course. Round both coefficients to 3 decimal places.
G. Draw the regression line on the grid above. (using the results from part E.)
H. Use the regression equation to predict the test B score for a student who had a test A score of 40. Show equation and work for credit.
I. What is the residual for student number 5? Did this student do better or worse than predicted on test B?
J. Why can't you predict a test B score for a student who had a test A score of 79?

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This solution is comprised of a detailed explanation of various aspects of Regression Analysis as it pertains to the given problem. Supplemented with Excel output and more than 300 words of text, this step-by-step explanation of this complicated topic provides a clear perspective of Regression Analysis.

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Please refer to the attachment for the solution.

A.

B. Correlation Coefficient, r = 0.91276
Coefficient of Determination, r^2 = 0.83313

C. The coefficient of determination gives the proportion of variability in a dataset that can be explained by the regression model. Thus, the proportion of variability in the given dataset that can be explained by this regression model is 0.83313.

D. The null hypothesis, states that there is no significant ...

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Anwesha Ghosh, MSc
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  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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