Question

please show work.

5. The manager of the Ramona Inn Hotel near Cloverleaf Stadium believes that how well the local Blue sox professional baseball team is playing has an impact on the occupancy rate at the hotel during the summer months. Following are the number of victories for the Blue Sox (in a 162 game schedule) for the past 8 years and the hotel occupancy rates: | Year Number of Blue Occupancy Rate Sox Wins (%) 83 70 78 85 86 75 85 87 90 89 93 92 7 87 8 91 Develop a linear regression model for these data, and forecast the occupancy rate for next year if the Blue Sox win 88 games. In addition, calculate r and r2 and interpret each one. Is this a good forecasting method for the given data?

Answer 1

Answer: To develop the linear regression Model the observing variable X is No. of Blue SOX wins. Y is the predicted variable of Occupancy rates.

Running a regression in Excel we get following output

we can write the equation as Y= 68.91895161 + 0.223387097*X

SUMMARY OUTPUT NO. Of Blue Sox Wins Line Fit Plot Regression Statistics Multiple R 0.411317094 R Square 0.169181752 Adjusted R Square 0.030712044 Standard Error 5.03216135 Observations Occupancy • Occupancy Predicted Occupancy ANOVA df Significance F 0.311349791 TT O 1 6 SS M SF 30.9391129 30.93911 1.221796 151.9358871 25.32265 182.875 0 20 Regression Residual Total 40 60 NO. Of Blue Sox Wins 80 100 7 Intercept NO. Of Blue Sox Wir Coefficients Standard Errort Stat P-value 68.91895161 16.56667189 4.160096 0.005944 0.223387097 0.202096463 1.105349 0.31135 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 28.38176583 109.45614 28.38176583109.4561374 -0.271125134 0.7178993 -0.271125134 0.717899327

If X=88 Games then Y (Occupancy) = 88.57 ~ 89

R squared here is 0.16918 which means only 16.92% of the variation in response variable Y is explained by this model which illustrates that the linear regression model might not be proper model to understand the relations between the given variables

R is 0.4113. It determines the correlation between the observed and predicted value. The low value the Occupancy rate is highly correlated with SOX wins.