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.

- 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?

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 |

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:

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:

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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