Task 1. A company publishes restaurant ratings for various locations. The accompanying data table contains the summated rating for food, dcor, service, and cost per person for a sample of 25 restaurants located in a city and 25 restaurants located in a suburb. Develop a regression model to predict the cost per person, based on the summated rating variable and a dummy variable concerning location (city versus suburban). Complete parts (a) through (n) below.

a. State the multiple regression equation that predicts the cost per person, based on the summated rating, X1, and the location, X2. Define X2 to be 0 for restaurants located in a city and let X2 be 1 for restaurants located in a suburb.

b. Interpret the regression coefficients in (a).

c. Predict the mean cost for a city restaurant with a summated rating of 60.

d. Perform a residual analysis on the results and determine whether the regression assumptions are satisfied. Which graph shows the residuals versus ?

Which graph shows the residuals versus X1?

Which graph shows the residuals versus X2?

Are the regression assumptions valid? Select all that apply. (There is a pattern in the plot of residuals versus X2. The regression assumptions are not valid. There are no patterns in any of the residual plots. The regression assumptions are valid. There is a pattern in the plot of residuals versus X1. The regression assumptions are not valid. There is a pattern in the plot of residuals versus predicted values. The regression assumptions are not valid).

e. Is there a significant relationship between price and the two independent variables (summated rating and location) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Find the slope of the simple linear regression equation that predicts cost per person from the summated rate. Compare the slope in (b) with this slope. Explain the difference in the results.

h. Compute and interpret the meaning of the coefficient of determination.

i. Compute and interpret the adjusted R2.

j. Find R2 value for the simple linear regression equation that predicts cost per person from the summated rate . Compare the two R2 values.

k. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model. State the multiple regression equation that predicts the selling price, based on the summated rating, X1, the location, X2, and the interaction term, X3=X1X2.

l. Test the interaction term, X3. State the conclusion.

m. On the basis of the results of (f) and (k), which model is the most appropriate? Explain.

n. What conclusions can you reach about the effect of the summated rating and the location of the restaurant on the cost of a meal?

Location	Cost	Summated Rating	Coded Location
City	28	50	0
City	89	77	0
City	28	54	0
City	65	71	0
City	57	72	0
City	38	61	0
City	44	54	0
City	66	68	0
City	33	58	0
City	76	72	0
City	29	51	0
City	61	67	0
City	39	53	0
City	46	57	0
City	75	66	0
City	51	58	0
City	45	51	0
City	31	49	0
City	68	60	0
City	72	64	0
City	33	53	0
City	43	53	0
City	44	57	0
City	46	63	0
City	94	79	0
Suburban	61	54	1
Suburban	51	64	1
Suburban	48	68	1
Suburban	29	56	1
Suburban	23	58	1
Suburban	44	59	1
Suburban	43	63	1
Suburban	20	47	1
Suburban	29	57	1
Suburban	26	54	1
Suburban	46	60	1
Suburban	60	58	1
Suburban	30	55	1
Suburban	54	69	1
Suburban	25	55	1
Suburban	54	58	1
Suburban	49	68	1
Suburban	28	55	1
Suburban	35	61	1
Suburban	56	67	1
Suburban	44	63	1
Suburban	22	51	1
Suburban	23	55	1
Suburban	51	68	1
Suburban	36	65	1