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Regression Analysis of Baseball Data Set

See data file attached.

Use the numerical data from the baseball data set (attached). For this assignment, you must have a hypothesis and have at least one independent variable (x) and the dependent variable (y) measured at the interval level. The assignment does not specify the type of regression used, so either bivariate or multiple regression is acceptable. We have been asked to develop one research question and formulate a hypothesis that may be tested with linear regression analysis (My team has chosen to research the linear correlation between ERA (batting average) and team wins to see if there is any relationship between the two).

Formulate a hypothesis statement regarding the research issue and perform a regression hypothesis test on the data

These questions should be answered:

1. Identify the dependent variable and your independent variable(s). State your a priori hypotheses about the sign (+ or −) of each predictor and your reasoning about cause and effect. Do you expect your independent variable(s) to have a positive or negative regression coefficient? Please be sure to make your hypothesis logical.

2. Does your sample size fulfill Evans's Rule (n/k ≥ 10) or at least Doane's Rule (n/k ≥ 5)? The 20:1 rule?

3. Perform the regression and include the estimated regression equation (round off to three significant digits for clarity). Do the coefficient signs agree with your a priori expectations?

4. Is the regression model significant? (Show the F table)

5. How would you describe the fit of this regression model? (Coefficient of determination or other relevant statistics.)

6. If you used multiple regression analysis, which independent variables are statistically significant predictors?

7. Are any assumptions of regression violated in your analysis? Why? (Be sure to run a normal probability plot, at the minimum.)


Solution Summary

The solution provides a detailed Regression Analysis of the given data. Regression Analysis (Correlation Coefficient, Coefficient of Determination, Covariance, Formulation of Regression Equation, Least Square Line, Scatter Plot , F-Table, Normal Probability Plot etc.) have been performed in EXCEL.