Question

44. Attendance 2016, revisited In Chapter 6, Exercise 45 looked at the relationship between the number of runs scored by Amer- ican League baseball teams and the average attendance at their home games for the 2016 season. Here are the scatterplot, the residuals plot, and part of the regression analysis for all major league teams in 2016 (National League teams in red, American League in blue): 45,000+ 37,500+ Average Home Attendance ::oti 750 Runs 825 15,000+ 7,500 Residuals Oto •: . -7,500 + 24,000 28,000 36,000 32,000 Predicted Response variable is: Home Avg Att R squared = 21.0% s= 7002 Variable Coefficient SE(Coeff) Intercept -12882.2 15815 Runs 59.389 21.75 a) Do you think a linear model is appropriate here? Explain. b) Interpret the meaning of R² in this context. c) Do the residuals show any pattern worth remarking on? d) The point at the top of the plots is the L.A. Dodgers. What can you say about the residual for the Dodgers?

Answer 1

a)

Since the scatterplot shows the linear trend for the data values, the linear model can be applied here.

b)

R-Square value

From, the result summary,

R Square

21%

The R-square value tells, how well the regression model fits the data values. The R-square value of the model is 21% which means, the model explains 21% of the variance of the data value. Based on this evidence we can conclude the model is not accurate since 79% variance of the data values is unexplained.

c)

From the residual vs predicted plot, we can see that the residual values are symmetrically distributed around the middle line (zero residual line) and we can not see any particular pattern in the residual. Hence the linear model is appropriate here since the residual values show homoscedasticity (equal variance).

d)

The residual value is defined as,

Residual = Observed – Predicted

The data point for L.A.Dodgers shows the highest positive residual which means the observed value is much greater than the predicted one. Hence the prediction is too low.