A magazine publishes restaurant ratings for various locations around the world.
ID: 3251972 • Letter: A
Question
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, service, and the cost per person. Develop a regression model to predict the cost perperson, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Use Excel and list the steps as you complete the parts below
Summated_Rating and Cost_($_per_person)
52 $38
66 $49
68 $60
67 $59
63 $43
59 $41
54 $44
64 $44
53 $32
49 $32
53 $42
52 $39
76 $89
63 $51
53 $37
50 $37
57 $34
44 $24
57 $40
58 $42
67 $64
62 $63
54 $25
73 $47
65 $46
Assuming a linear relationship, use the least-squares method to compute the regression coefficients
b0 and b1.
Interpret the meaning of the Y-intercept, b0, and the slope, b1.
Predict the mean cost per person for a restaurant with a summated rating of 40.
Explanation / Answer
The Regression Output
So linear equation
y = -39.70 + 1.43x
where y = cost per person
x = Cost ($ per person)
Here b0 = -39.70 and b1 = 1.43
The mean cost per person with summated rating of 40
y = -39.70 + 1.43 * 40 = $17.5
SUMMARY OUTPUT Regression Statistics Multiple R 0.813823 R Square 0.662307 Adjusted R Square 0.647625 Standard Error 8.28636 Observations 25 ANOVA df SS MS F Significance F Regression 1 3097.373 3097.373 45.10928 7.5E-07 Residual 23 1579.267 68.66377 Total 24 4676.64 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -39.6999 12.70172 -3.12555 0.004751 -65.9754 -13.4244 Summated Ratings 1.42968 0.212866 6.716344 7.5E-07 0.989334 1.870027Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.