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QMB3200 - Homework 3– Ch 14 & 15– spring 2018

70 points - Due april 8, 2018

1) (32pt) Starting salaries for accountants in Tampa follow those of many U.S. cities. The table bellow shows starting salaries (in thousands of dollars) and the cost of living index for 5 metropolitan areas. A regression analysis will help provide explanation on how cost of living explains salary in this sample.

a. (4pt) Explain what the scatter diagram for cost of living

and salary indicates about the relationship of these

variables

b. (10pt)Use the least squares method (OLS) to develop an estimated regression equation for this problem (That is, calculate bo and b1)

Metropolitan area	Index	Salary (thousand $)
Oklahoma City	46	19
Tampa	35	10
Atlanta	50	27
Sacramento	65	29
Honolulu	59	25
Mean	51.0	22.0

c. (2pt) Write down the estimated regression equation.

d. (4pt)Provide an interpretation for the slope.

e. (10pt)Provide an interpretation for the intercept of the estimated regression equation.

f. (2pt) Comment on the normality assumptions of Model given the Residual plot below.

In Model

2. (38pt) Consider the following data sample from the Consumer Report on Restaurant Satisfaction. The variable TYPE indicates whether the restaurant is Italian or Seafood/steakhouse. The variable PRICE indicates average amount paid per person for dinner and drinks. The variable SCORE reflects diner’s overall customer satisfaction, with higher values indicating greater satisfaction (100 is completely satisfied). A regression analysis is conducted in several steps to find out whether type of restaurant and price explains Score (customer’ satisfaction).

Restaurant	Price ($)	Score	Type of restaurant
Bertucci's	16	77	Italian
Black Angus	24	79	Seafood/Steak
Bonefish Grill	26	85	Seafood/Steak
Bravo!cuccina italiana	18	84	Italian
Buca di Beppo	17	81	Italian
Bugaboo Steak House	18	77	Seafood/Steak
Carrabba's Italian grill	23	86	Italian
Brown's Steakhouse	17	75	Seafood/Steak
Il Fornaio	28	83	Italian
Joe's crab Shack	15	71	Seafood/Steak
Johnny Carino's Italian	17	81	Italian
Lone Star SteakHouse	17	76	Seafood/Steak
Longhorn steakhouse	19	81	Seafood/Steak
Maggio's little Italy	22	83	Italian
McGrath's Fish House	16	81	Seafood/Steak
Oliven Graden	19	81	Italian
Outback Steakhouse	20	80	Seafood/Steak
Red Lobster	18	78	Seafood/Steak
Romano's macorroni grill	18	82	Italian
The old spaguetti factory	12	79	Italian
Uno Chicago Grill	16	76	Italian

a. (3pt) Comment on the scatter diagram for the variables price and score.

b. (2pt) How do you include the variable TYPE of restaurant in a regression model?

MODEL 1- includes only the variable PRICE to explain SCORE

a. (2pt) Comment on the goodness of fit of MODEL 1.

b. (2pt) Report the statistical significance of MODEL 1

MODEL 2 – Include the dummy variable DTYPE which takes value 1 if Italian restaurant, 0 otherwise

a. (2pt) Comment on the goodness of fit of MODEL 2.

b. (4pt) Report the statistical significance of the coefficients for MODEL 2

c. (3pt) How important you think the variable DTYPE is in explaining SCORE?

d. (2pt) Write down the estimated regression equation for this model.

e. (6pt) Interpret the intercept for Model 2.

f. (3pt) Interpret the coefficient for the variable DTYPE.

g. (2pt) interpret the coefficient for the variable Price.

h. (2pt) Curvature from the data is captured by a quadratic and a cubic model using only PRICE as explanatory variable. Regression analysis results are shown in table below. If considering previous MODEL 1, MODEL 2 and the quadratic and cubic models below, which one you think fits the data best? Explain why.

i. (3pt) Write down the quadratic model equation.

j. (2pt) What is the average SCORE in the quadratic model?

Salary in

Thousands $

Cost of Living Index