Question

In: Operations Management

1. The managers of the Ada Hotel forecast the breakfast covers based on number of guest...

1. The managers of the Ada Hotel forecast the breakfast covers based on number of guest rooms. Following table presents the number of rooms sold and breakfast covers for the past year, 2017.
Room Guests Breakfast Covers
January 1,200 1,400
February 1,020 1,220
March 1,250 1,420
April 1,100 1,320
May 1,380 1,520
June 1,400 1,580
July 1,520 1,650
August 1,550 1,690
September 1,450 1,400
October 1,210 1,380
November 1,080 1,240
December 1,050 1,220
Required:
1. Determine the coefficient of correlation and coefficient of determination for the Ada Hotel based on the data presented above. Comment on the strength of the relationship between room guests and breakfast covers.
2. Determine a regression equation for forecasting breakfast covers based on the number of room guests.
3. If 1,620 room guests are forecasted for next January, how many breakfast customers are forecasted to be served?
Note: You need to use MS Excel’s regression function to answer these questions. Please attach your regression output (Summary Output) to your submission.

Solutions

Expert Solution

Here Y (Breakfast Cover) is the dependent Varialbe & X (Room Guests) is independent variable

Put the data in X & Y Column in Excel > go to data Tab > click data Analysis > select X&Y input range > select the plot> you will get following output.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.932347
R Square 0.86927
Adjusted R Square 0.856197
Standard Error 61.16764
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 248785.2 248785.2 66.49378 9.96E-06
Residual 10 37414.81 3741.481
Total 11 286200
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 403.773 125.8683 3.207901 0.009365 123.321 684.225 123.321 684.225
X Variable 1 0.801757 0.098322 8.154372 9.96E-06 0.582681 1.020833 0.582681 1.020833

1. Step 1 : Run a regression equation, then following output will be observed

As per data set, and total number of XY pair is 12

Output equation is as below

Y= Slope + Co-efficient of co-relation (r) * X

Y= 403.8 + 0.8018*X

Co-efficient of correlation ( r )= 0.8018

Co- efficient of determination = (r)^2 = 0.6423

Therefore 64.23% is the likelihood of forecast with this model to be accurate

Strenght of relationship is good as the r value is more than 0.8.

2. Regression equation is as below

Y= Slope + Co-efficient of co-relation (r) * X

Y= 403.8 + 0.8018*X

3. X=1620 then we will have to calculate the Y as per equation above

Y= 403.8 + 0.8018*1620 = 1702.7 = 1703

keosha answered 5 months ago
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