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Posts: 193
3 weeks ago
A sports analyst was interested in finding out how well a football team's winning percentage (stated as a proportion) can be predicted based upon points scored and points allowed. She selects a random sample of 15 football teams. Each team played 10 games. She decided to use the point differential, points scored minus points allowed as the predictor variable. The data are shown in the table below, and regression output is given afterward.


 
Is there evidence of an association between Point Differential and Winning Percentage? Test an appropriate hypothesis and state your conclusion in the proper context.
Textbook 

Stats: Modeling the World


Edition: 4th
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Posts: 245
3 weeks ago
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We have Winning Percentage and Point Difference from a random sample of 15 teams. We want to know if there is an association between Winning Percentage and Point Difference.
H0: There is no association between Winning Percentage and Point Difference. β1 = 0
HA: There is an association between Winning Percentage and Point Difference. β1 ≠ 0

*Straight enough condition: There is no obvious bend in the original scatterplot of the data or in the plot of the residuals against the predicted values..
*Independence: These data were not collected over time and there is no pattern in the residuals plot.
*Does the plot thicken?: Neither the original scatterplot nor the residual plot shows any changes in the spread about the line.
*Nearly Normal condition: With the exception of a possible outlier, the histogram of the residuals is roughly unimodal and symmetric.
Under these conditions the regression model is appropriate. We will use the linear regression t-test.
Regression equation: = 0.518 + 0.00495(PointDiff)
The R2 for the regression is 80.8%. Point Difference seems to account for about 81% of the variability in Winning Percentage. The regression equation indicates that each additional 10 points in Point Difference corresponds to an increase in the Winning Percentage of about 0.05, on average.
The P-value < 0.0001 is very small, so we reject the null hypothesis. There is strong evidence of an association between Winning Percentage and Point Difference.
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3 weeks ago
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