Statistical Analysis of Football Data: Points/Game and Yards/Game

This assignment presents a statistical analysis of football data, specifically examining the relationship between points per game and yards per game. The analysis begins with a check of assumptions, confirming linearity, normality of errors, homoscedasticity, and independence of errors. A scatter plot reveals a positive linear relationship, followed by the identification of outliers. Regression analysis is performed to predict points per game based on yards per game, with an R-squared value of 0.711 indicating that 71.1% of the variation in points per game is explained by yards per game. The ANOVA table confirms the significance of the overall regression model. Finally, the regression coefficients are analyzed, showing that both the intercept and the independent variable (yards per game) are significant at the 5% level, with a unit increase in yards per game expected to increase points per game by 0.1229. The assignment includes tables summarizing the regression statistics, ANOVA results, and regression coefficients.

Problem Analysis and Statistics
Student Name:
Instructor Name:
Course Number:
4th September 2019

Checking assumptions
 Linearity can be assumed
 The data is linear
 Normality of errors can be assumed
 The histogram of errors can be assumed
 Homoscedasticity can be assumed
 The variation about the regression line is constant for all values of the independent variable
 Independence of errors can be assumed
 The residuals are independent for each value of the independent variable
 Therefore, the assumptions are met.
Scatter plot
The scatter plot below shows that there is a positive linear relationship between Yards per game and
Points per game. An increase in the Yards per game is expected to result in an increase in the Points per
game.
Figure 1: Scatter plot of Points/Game against Yards/Game
Outliers
From the above graph, we can see that there are two outliers
Regression analysis
A regression analysis was performed to try and predict the Points per game based on the Yards per
game. Results are presented below;
The summary output table shows that the value of R-square is 0.711; this implies that 71.1% of the
variation in the Points per game is explained by the Yards per game.

Table 1: SUMMARY OUTPUT
Regression Statistics
Multiple R 0.843181
R Square 0.710955
Adjusted R Square 0.70132
Standard Error 2.869583
Observations 32
Table 2: ANOVA
df SS MS F Significance F
Regression 1 607.6236 607.6236 73.78994 1.39E-09
Residual 30 247.0351 8.234505
Total 31 854.6588
The ANOVA table above shows the p-value for the F-Statistics to be 0.000 (a value less than 5% level of
significance), we therefore reject the null hypothesis and conclude that the overall regression model is
significant at 5% level of significance.
Table 3: Regression coefficients
Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Intercept -18.2288 4.682343 -3.8931 0.000512 -27.7915 -8.66621
Yards/Game 0.122941 0.014312 8.590107 1.39E-09 0.093712 0.15217
Lastly, the above table (table 3) presents the regression coefficients. As can be seen both the intercept
and the independent variable (Yards/Game) are significant in the model at 5% level of significance (p <
0.05).
The coefficient of Yards/Game is 0.1229; this implies that a unit increase in the Yards/Game is expected
to result in an increase in the Points/Game by 0.1229. Similarly, a unit decrease in the Yards/Game is
expected to result in a decrease in the Points/Game by 0.1229.