Zagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service.Predict the mean cost per person for a restaurant with a sum-mated rating of 50.What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?LocationFood DécorServiceSummated RatingCoded LocationCost BinsMidpointsCity22141955033 19.9925City20152055026 29.9935City23192163043 39.9945City19181855032 49.9955City24161858044 59.9965City22222165044 69.9975City22202062050 79.9985City20191958042 89.99 City21171957044   City20181856036   City23222469061   City20192059050   City21192161051   City24192164050   City25232371076   City22212164053   City23152260044   City26222472077   City21232165057   City24151958043   City21151955029   City23161655034   City25212672077   City22202163050   City26252475074   City23212165056   City22191758067   City26202369057   City26232574066   City24232471080   City22232368068   City24162363042   City20171956048   City25192367060   City23202164035   City21192262045   City20161854032   City23151856025   City26242474074   City21181857043   City22161957039   City19232163055   City24192164065   City23162059035   City24262272061   City21171856037   City21171957054   City23192264041   City23192163033   City23141956027   Suburban24202266147   Suburban22182262148   Suburban18131849135   Suburban22232065159   Suburban22182464144   Suburban23252472151   Suburban20121850137   Suburban19181956136   Suburban22192162143   Suburban27212775152   Suburban19141851134   Suburban22111952138   Suburban24222470151   Suburban19151953134   Suburban21232165151   Suburban21192161134   Suburban23192365151   Suburban23202265156   Suburban21131953126   Suburban24192265134   Suburban20182058134   Suburban24222470144   Suburban23172262140   Suburban23162160131   Suburban23182263154   Suburban19122253141   Suburban22172160150   Suburban26272477171   Suburban22212366160   Suburban19151751137   Suburban21122053127   Suburban26182266134   Suburban22252168148   Suburban21212163139   Suburban20202060144   Suburban22182262141   Suburban23201962137   Suburban24212368147   Suburban23272272167   Suburban24242270168   Suburban26172467149   Suburban22221963129   Suburban24182264133   Suburban20192059139   Suburban26192368139   Suburban22152158128   Suburban18201856146   Suburban26272578170   Suburban25262374160   Suburban22252269152

Question
Asked Nov 28, 2019
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Zagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service.

  1. Predict the mean cost per person for a restaurant with a sum-mated rating of 50.
  2. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?
Location Food  Décor Service Summated Rating Coded Location Cost   Bins Midpoints
City 22 14 19 55 0 33   19.99 25
City 20 15 20 55 0 26   29.99 35
City 23 19 21 63 0 43   39.99 45
City 19 18 18 55 0 32   49.99 55
City 24 16 18 58 0 44   59.99 65
City 22 22 21 65 0 44   69.99 75
City 22 20 20 62 0 50   79.99 85
City 20 19 19 58 0 42   89.99  
City 21 17 19 57 0 44      
City 20 18 18 56 0 36      
City 23 22 24 69 0 61      
City 20 19 20 59 0 50      
City 21 19 21 61 0 51      
City 24 19 21 64 0 50      
City 25 23 23 71 0 76      
City 22 21 21 64 0 53      
City 23 15 22 60 0 44      
City 26 22 24 72 0 77      
City 21 23 21 65 0 57      
City 24 15 19 58 0 43      
City 21 15 19 55 0 29      
City 23 16 16 55 0 34      
City 25 21 26 72 0 77      
City 22 20 21 63 0 50      
City 26 25 24 75 0 74      
City 23 21 21 65 0 56      
City 22 19 17 58 0 67      
City 26 20 23 69 0 57      
City 26 23 25 74 0 66      
City 24 23 24 71 0 80      
City 22 23 23 68 0 68      
City 24 16 23 63 0 42      
City 20 17 19 56 0 48      
City 25 19 23 67 0 60      
City 23 20 21 64 0 35      
City 21 19 22 62 0 45      
City 20 16 18 54 0 32      
City 23 15 18 56 0 25      
City 26 24 24 74 0 74      
City 21 18 18 57 0 43      
City 22 16 19 57 0 39      
City 19 23 21 63 0 55      
City 24 19 21 64 0 65      
City 23 16 20 59 0 35      
City 24 26 22 72 0 61      
City 21 17 18 56 0 37      
City 21 17 19 57 0 54      
City 23 19 22 64 0 41      
City 23 19 21 63 0 33      
City 23 14 19 56 0 27      
Suburban 24 20 22 66 1 47      
Suburban 22 18 22 62 1 48      
Suburban 18 13 18 49 1 35      
Suburban 22 23 20 65 1 59      
Suburban 22 18 24 64 1 44      
Suburban 23 25 24 72 1 51      
Suburban 20 12 18 50 1 37      
Suburban 19 18 19 56 1 36      
Suburban 22 19 21 62 1 43      
Suburban 27 21 27 75 1 52      
Suburban 19 14 18 51 1 34      
Suburban 22 11 19 52 1 38      
Suburban 24 22 24 70 1 51      
Suburban 19 15 19 53 1 34      
Suburban 21 23 21 65 1 51      
Suburban 21 19 21 61 1 34      
Suburban 23 19 23 65 1 51      
Suburban 23 20 22 65 1 56      
Suburban 21 13 19 53 1 26      
Suburban 24 19 22 65 1 34      
Suburban 20 18 20 58 1 34      
Suburban 24 22 24 70 1 44      
Suburban 23 17 22 62 1 40      
Suburban 23 16 21 60 1 31      
Suburban 23 18 22 63 1 54      
Suburban 19 12 22 53 1 41      
Suburban 22 17 21 60 1 50      
Suburban 26 27 24 77 1 71      
Suburban 22 21 23 66 1 60      
Suburban 19 15 17 51 1 37      
Suburban 21 12 20 53 1 27      
Suburban 26 18 22 66 1 34      
Suburban 22 25 21 68 1 48      
Suburban 21 21 21 63 1 39      
Suburban 20 20 20 60 1 44      
Suburban 22 18 22 62 1 41      
Suburban 23 20 19 62 1 37      
Suburban 24 21 23 68 1 47      
Suburban 23 27 22 72 1 67      
Suburban 24 24 22 70 1 68      
Suburban 26 17 24 67 1 49      
Suburban 22 22 19 63 1 29      
Suburban 24 18 22 64 1 33      
Suburban 20 19 20 59 1 39      
Suburban 26 19 23 68 1 39      
Suburban 22 15 21 58 1 28      
Suburban 18 20 18 56 1 46      
Suburban 26 27 25 78 1 70      
Suburban 25 26 23 74 1 60      
Suburban 22 25 22 69 1 52      
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Expert Answer

Step 1

(1)

Step-by-step procedure to obtain the regression equation using MINITAB:

Step 1: Choose Stat > Regression > Regression.

Step 2: In Response, enter the column containing the response (Y) variable as Cost.

Step 3: In Predictors, enter the columns containing the predictor (X) variables as Summated Rating.

Step 4: Click OK.

Output using the MINITAB software is given below:

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Regression Analysis: Cost versus Summated Rating Analysis of Variance DF Adi SS Adj MS F-Value P-Value Source Regression 0.000 1 9740 9740.06 117.77 Summated Rating 117.77 0.000 1 9740 9740.06 Error 98 8105 82.70 Lack-of-Fit 26 1976 75.98 0.89 0.616 Pure Error 72 6129 85.13 Total 99 17845 Model Summary R-sa R-sqladi) R-sqlpred) 9.09400 54.58% 54.12% 52.77% Coefficients Coef SE Coef T-Value P-Value Term VIF -46.77 Constant 8.67 5.39 0.000 Summated Rating 1,496 10.85 0.138 0.000 1.00 Regression Equation Cost= -46.77+ 1.496 Summated Rating Fits and Diagnostics for Unusual Observations Resid Std Resid Obs Cost Fit 26.99 27 67.00 40.01 2.99 R 2.29 R 30 80.00 5946 20.54 92 29.00 4749 -18.49 2.04 R 98 70.00 69.94 0.06 001 R Large residual x Unusual X

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Step 2

The Predicted value for the mean cost per person for a restaurant with a sum-mated rating of 50 is $28.03 and it is obtained as follows:

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Cost 46.77+1.496 Summated Rating =- 46.77 +1.496 (50) - 28.03

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Step 3

(2)

Step-by-step procedure to obtain the scatterplot using MINITAB:

Step 1: Choose Graph > Scatter plot.

Step 2: Choose Simple, and then click OK.

Step 3: Under Y variables, enter a column of Cost.

Step 4: Under X variables, enter a colum...

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Scatterplot of Cost vs Summated Rating 80 70 60 50 30 20 50 55 60 65 70 75 80 Summated Rating Cost 40

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