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Regression & Forecasting

Regression & Forecasting

  1. In major league baseball, the National League consists of 16 teams. Below is the number of victories of each team in the 2006 season over a 162 game season along with each team’s seasonal payroll. Using the regression model results below to predict the number of victories based on the seasonal payroll. Using regression analysis questions below, discuss the effectiveness of this model.

 

Team               Payroll ($M)                Victories

 

Mets                 117                              97

Astros              108                              82

Dodgers           107                              88

Cubs                99                                66

Giants              99                                76

Cardinals         96                                83

Phillies             93                                85

Braves             92                                79

Padres              74                                88

Nationals         67                                71

Reds                64                                80

Diamondb        61                                76

Brewers           58                                75

Rockies                        53                                76

Pirates              43                                67

Marlins                        21                                78

 

 

 

SUMMARY OUTPUT

             
                 
Regression Statistics              
Multiple R 0.489786              
R Square 0.239891              
Adjusted R Square 0.185597              
Standard Error 7.251199              
Observations 16              
                 
ANOVA                
  df SS MS F Significance F      
Regression 1 232.3191 232.3191 4.418402 0.054133      
Residual 14 736.1184 52.57989          
Total 15 968.4375            
                 
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 67.82032 5.703551 11.89089 1.05E-08 55.58741 80.05323 55.58741 80.05323
X Variable 1 0.145268 0.069109 2.101999 0.054133 -0.00296 0.293492 -0.00296 0.293492
                 

 

  1. Find (specify) the best model to predict MLB team victories.
  2. Predict team victories based on a team payroll of $101M.
  3. How well does the model explain victories? Discuss in detail.
  4. Is the model significant? Test at the critical value of 3.70.
  1. Marriott Corporation is considering building a new hotel conference center on a beachfront area of Venezuela. Before choosing the final location for the hotel/conference center complex, the management team acquired occupancy data and measured the proximity to the beach and hotel age for 14 existing hotels in the area. The management team recognizes that the relationship between distance from the beach, age and occupancy rate must be known in order to predict the success of the new complex. The data are as follows.
Hotel Distance Age (years) Occupancy rate
1 0.1 3 92
2 0.1 10 95
3 0.2 2 96
4 0.3 1 90
5 0.4 3 89
6 0.4 3 86
7 0.5 1 90
8 0.6 7 83
9 0.7 18 85
10 0.7 4 80
11 0.8 18 78
12 0.8 25 76
13 0.9 30 72
14 0.9 40 75

 

SUMMARY OUTPUT              
                 
Regression Statistics              
Multiple R 0.94970074              
R Square 0.9019315              
Adjusted R Square 0.88410087              
Standard Error 2.61045721              
Observations 14              
                 
ANOVA                
  df SS MS F Significance F      
Regression 2 689.3977875 344.69889 50.58325 2.8406E-06      
Residual 11 74.95935534 6.8144868          
Total 13 764.3571429            
                 
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 97.6817524 1.598195795 61.120016 2.783E-15 94.1641472 101.19936 94.164147 101.19936
Variable 1 -22.166615 3.870652263 -5.7268422 0.0001328 -30.6858629 -13.647367 -30.685863 -13.647367
Age -0.1000702 0.088049151 -1.1365267 0.2798899 -0.29386509 0.0937247 -0.2938651 0.0937247

 

  1. Find (identify) the best model to predict the occupancy rate of the hotel complex.
  2. Predict occupancy based on a 5 year old hotel located 0.65 miles from the ocean.
  3. How well does the model explain occupancy? Discuss in detail
  4. Is the model significant? Test this assertion. The critical value of F is 3.98.

 

 

 

  1. Due to increased world demand for the automobile, Ferrari Corporation made the decision to increase production of its high end car. In Shanghai China alone, sales of Ferraris have continued to grow steadily over the past several years. Data below indicate the growth in demand for this car in this city over the past 5 years.

 

Year                 Sales

1                      4.5

2                      4.9

3                      5.2

4                      5.6

5                      5.8

6                      5.9

7                      ?

 

The regional sales manager has predicted that even before the car was introduced in China, year one sales were backordered by 410 cars.

 

  1. Use a three year moving average forecasting model to forecast the sales of Ferraris.

 

  1. Use a three year weighted moving average forecasting model to forecast the sales of Ferraris with weights of 2 1 1.

 

  1. Using exponential smoothing with a coefficient of smoothing of 0.3, develop forecasts for years 2 through 7.

 

  1. Evaluating the outcomes of the three methods using MAD. Would you use exponential smoothing with a smoothing constant of 0.3, a three year moving average, or a weighted moving average, to predict the future sale of Ferraris?

 

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