DNSC 2001 –Business Analytics II – Spring 2023 Assignment 3
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DNSC 2001 – Business Analytics II – Spring 2023
Assignment 3
Question 1:
A marketing professor is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 100 students who took the course last semester are provided in the file MktHrsPts-100-S21.xlsx.
a. Develop an estimated regression equation showing how total points earned is related to hours spent studying. What is the estimated regression model?
b. Test whether each of the regression parameters F0 and F1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
c. How much of the variation in the sample values of total point earned does the model you estimated in part a explain?
d. Mark Sweeney spent 95 hours studying. Use the regression model you estimated in part a to predict the total points Mark earned.
Question 2:
FBStyles, Inc. sells cosmetic products in the US. The marketing department of FBStyles, Inc. claims that there exits a positive linear relationship between the advertising expenditures and the cosmetics sales. The marketing department recently analyzed the sales of FBStyles' products over a period of 42 weeks. For each week in the sample, FBStyles' sales (SALES) and their advertising expenditures (ADVERT) were recorded. A simple regression analysis was made using this data and the model:
SALES = 0 + 1 ADVERT +
The resulting JMP IN output is given below. Note that some parts of the output are deleted on purpose and some of the results are left as"?".
Response (Dependent variable): SALES
Parameter Estimates
Term
Intercept
ADVERT
Estimate
483.402
1.43629
Std Error
157.128
0.149238
t Ratio
?
9.62
Analysis of Variance
Sum of
Source
Model
Error
C Total
Squares
14,123,027
?
20,222,069
D.F.
?
?
41
(a) Fill out all results in the output denoted by "?".
(b) What is the interpretation of 1 in the context presented here ? Be precise.
(c) Using the results given, what can you say about the marketing department's claim? Please state the corresponding hypotheses symbolically and test the claim at = 0.05 level.
(e) Based on the analysis, what is your prediction (estimate) of FBStyles' sales if the advertising expenditures is $ 10,000?
(g) Assume that in week 40, the actual sales was observed as $16,505 when the level of advertising expenditures for the week was $10,000. What is the correi ianlg (error) from the regression model for week 40 sales?
(i) Obtain R2 for the model.
As an alternative to the above simple regression model, a market researcher proposed
the following model
SALES = 0 + 1 ADVERT + 2 COMPSALES +
where COMPSALES is the sales of FBStyles' main competitor over the 42 week period. The corresponding JMP IN output is given below.
Response: SALES
Summary of Fit
Rsquare
RsquareAdj
Root Mean Square Error Mean of Response
0.828993
0.820223
297.7748
1880.024
Observations (or Sum Wgts) 42
Parameter Estimates
Term Estimate Std Error t Ratio Prob>|t|
Intercept 17787.977 3173.078 5.61 <.0001
ADVERT 0.7772986 0.16593 4.68 <.0001
COMPSALES -17.44219 3.196029 -5.46 <.0001
(j) What is the interpretation of the 1 under the new model ? Which model would you use to predict FBStyles' Sales ? Explain why.
(k) Obtain the Rsquare between the actual and predicted SALES under the new model
in (j).
Question 3: The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the data for 225 compact, midsized, and large cars follows. The Class column identifies the size of the car; Compact, Midsize, or Large. The Displacement column shows the engine’s displacement in liters. The FuelType column shows whether the car uses premium (P) or regular (R) fuel, and the HwyMPG column shows the fuel efficiency rating for highway driving in terms of miles per gallon. The complete data set is contained in the file FuelData-225.xlsx. :
a. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine’s displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? (The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize and the value of ClassLarge are both 0. The value of FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel.)
b. For the estimated regression equation developed in part a, check for the significance of an overall regression relationship and relationships between each of the independent variables and the dependent variable using the 0.05 level of significance.
Part 2
Question 4: In a study of housing demand, a county assessor is interested in developing a regression model to estimate the selling price of residential properties within her jurisdiction. She randomly selects 15 houses and records the selling price in addition to the following values: the size of the house (in hundreds of square feet), the total number of rooms in the house, the age of the house, and an indication of whether the house has an attached garage. These data are listed in the file Housing.xlsx.
a. Estimate a multiple regression equation using all of the available explanatory variables to predict the selling price of residential properties.
b. Do you see any evidence of multicollinearity in this model? Explain.
c. Now run a simple linear regression using the variable that has the highest correlation with the selling price.
d. Compare results of both models and summarize your findings.
Question 5:
Analyze the Servpro case using a multiple regression model and interpret the model results using a subset of the data posted along with this assignment.
2023-05-08