37. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 1

Question

37. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website, February 11, 2009) Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfac- tion. A score of 80 can be interpreted as very satisfied. Score Restaurant Bertucci's Black Angus Steakhouse Bonefish Grill Bravo! Cucina Italiana Buca di Beppo Bugaboo Creek Steak House Type Italian Seafood/Steakhouse Seafood/Steakhouse Italian Italian Price ($) 16 24 26 18 17 18 gs 85 84 81 Seafood/Steakhouse (continued)

Explanation / Answer

There are 2 predictor variables: The type of Restraunt which is a binary variable taking 2 values : Italian (say X1 take value = '1') and Seafood/Steakhouse (say X1 take value = '0') . The second predictor is the price spent (say X2).

Y is the overall score and the regression equation we want to fit is of form:

Y = a + b1*X1 + b2*X2

To estimate a,b1,b2 we use Gauss-Markov theorem and conclude that the parameter estimate vector of (a,b1,b2) is given by (X'X)-1X'Y where X is the design matrix i.e. contains the values of the predictor variables and Y is the vector containing the dependant variable values.

We solve for (X'X)-1X'Y in Excel (Data analysis toolpack -> Regression) and the parameter estimates obtained are:

a= 67.40

b1= 3.04

b2= 0.57

So the required regression equation is :

Y = 67.4 + ( 3.04 * X1 ) + ( 0.57 * X2 )

(b) Given X1 = 0 and X2 = 20, then predicted value of Y is 67.4 + (3.04*0) + (0.57*20) = 78.4

If the restraunt becomes an Italian restraunt then the customer score increase by 3.04 which is the regression coefficient of X1.

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