Given the following data use Excel to construct a least square regression model

ID: 3207315 • Letter: G

Question

Given the following data use Excel to construct a least square regression model that develops a religion between the number should game rainy days, and the team payroll of the Winterville Indians baseball team. The model should predict future lost games. What is the regression equation? What are expected games lost if Winterville experiences 15 rainy days and has a payroll of $200? What is the model's correlation coefficient and coefficient of determination? Interpret and discuss these values. What are the model's R, F, and t statistics? Comment on their outcomes. Run tests for multicollinearity, autocorrelation, and heteroscedasticity. Comment on the outcomes.

Explanation / Answer

Follow the steps to cocmpute the output.

Enter data in Excel-Data-Data Analysis-Regression-type A1:A11 in Input X range-enetr B1:C11 in input Y range-enter F4 in output range-Type Ok.

a. The regression equation is as follows:

Games lost=61.3876-0.0396 Rainy days-0.2086 Payroll

b. Substitute, Rainy days with 15 and Payroll with 200 in the given equation to obtain the Games lost.

Games lost=61.3876-0.0396*15-0.2086*200

=19.0736

~19 (ans)

c. Assuming Rainy season and Payroll to be independent variables, and Games lost to be dependent one, the multiple correlation coefficient is given by

r gameslost,rainyseason payroll=0.98

The R^2 is 0.9613. Rainy season and Payroll together account for about 96.13% variation in Games lost for Winterville Indians Baseball team.

d. The model's F statistic, F(2,8)=99.56, p<0.05 is signficant. Therefore, reject overall H0 (H0: beta1=beta2=...=betak=0), atleast one of the slope coeffciients is not zero.

Now test the null hypothesis for each of the coefficients of the form.

H0: the jth variable contributes nothing useful after allowing for other predictor in the model:betaj=0

HA:the jth variable makes a useful contribution to the model., betaj=/=0

Both the variable, rainy season and payroll have small t ratios, with payroll being the significant one with p value less than 0.05. Therefore, payroll contributes significantly to the model.

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Given the following data use Excel to construct a least square regression model

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