The manager of the Commander Hotel near City 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 eight years and the hotel occupancy rates:

Year

Number of Blue Sox Wins

Occupancy Rate

1

70

81%

2

65

74

3

81

83

4

88

84

5

80

85

6

92

91

7

83

88

8

64

80

Develop a linear regression model for these data, and forecast the occupancy rate for next year if the Blue Sox win 85 games. Does there appear to be a strong relationship between wins and occupancy rate?

provided in the explanation segment

Explanation:

we will be expressing t the linear regression as thus:

Y = a + b.t

 given;

Y ( dependent variable ) = Occupancy rate

T ( independent variable) = Number of blue sox wins

A,b are  Constants

We now put all the values of the number of blue sox wins and occupancy rates in two parallel columns and apply the formula LINEST ( ) in excel.

Accordingly, we obtain values of a, b which are as per the following :

A = 49.946

B = 0.4276

From this we say, Y =49.946 + 0.4276.t

Value of Y when Blue sox wins = 85 games :

Y = 49.946 + 0.4276X85 = 49.946 +36.346 =86.292

Given the Occupation Rate For Next Year as 86.292 %

In order to find out the degree of correlation between these 2 sets of data,we apply the formula CORREL () in excel and obtain value = 0.8626

Therefore the Maximum value of correlation coefficient = 1.

Conclusively, we can say that there is a very high degree of correlation i.e. strong relationship between wins and occupancy rate

cheers i hope this helps

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