Stock Market and Fuel Efficiency Analysis
Budget: $30 – $250 USD
Assignment 5 (MBA 693)
Submission guidelines:
• The assignment has 2 questions, and you can use either Excel or JMP to complete it. If you are
using Excel, submit your answers in Excel, if you are using JMP, submit your output screenshots in
a Word File.
• If you submit multiple files, only the file with the latest time stamp would be graded.
• Label your work clearly.
Problem 1: Stock Market Performance.
The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are
used as measures of overall movement in the stock market. The DJIA is based on the price
movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say
the S&P 500 is a better measure of stock market performance because it is broader based. The
closing price for the DJIA and the S&P 500 for 15 weeks of a previous year follow (Barron’s web
site).
a) Develop a scatter chart for these data with DJIA as the independent variable. What does
the scatter chart indicate about the relationship between DJIA and S&P 500?
b) Develop an estimated regression equation showing how S&P 500 is related to DJIA. What
is the estimated regression model?
c) What is the 95% confidence interval for the regression parameter β1? Based on this
interval, what conclusion can you make about the hypotheses that the regression
parameter β1 is equal to zero?
d) What is the 95% confidence interval for the regression parameter β0? Based on this
interval, what conclusion can you make about the hypotheses that the regression
parameter β0 is equal to zero?
e) How much of the variation in the sample values of S&P 500 does the model estimated in
part (b) explain?
f) Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the
S&P 500.
g) Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value
in part (f) is beyond the range of the DJIA used to develop the estimated regression
equation?Problem 2: Estimating Fuel Mileage by Car Size.
The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and
trucks. A portion of the data for 311 compact, midsized, and large cars is given to you. 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.
a) Develop an estimated regression equation that can be used to predict the fuel efficiency
for highway driving given the engine’s displacement. Test for significance using the 0.05
level of significance. How much of the variation in the sample values of HwyMPG does
this estimated regression equation explain?
b) Create a scatter chart with HwyMPG on the y-axis and displacement on the x-axis for
which the points representing compact, midsize, and large automobiles are shown in
different shapes and/or colors. What does this chart suggest about the relationship
between the class of automobile (compact, midsize, and large) and HwyMPG?
c) Now consider the addition of the dummy variables ClassMidsize and ClassLarge to the
simple linear regression model in part (a). 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. Develop the estimated regression equation that can be used to predict the
fuel efficiency for highway driving, given the engine’s displacement and the dummy
variables ClassMidsize and ClassLarge. How much of the variation in the sample values of
HwyMPG is explained by this estimated regression equation?
d) Use significance level of 0.05 to determine whether the dummy variables added to the
model in part (c) are significant.
e) Consider the addition of the dummy variable FuelPremium, where the value of
FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. 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?
f) For the estimated regression equation developed in part (e), test for the significance of
the relationship between each of the independent variables and the dependent variable
using the 0.05 level of significance for each test.
Submission guidelines:
• The assignment has 2 questions, and you can use either Excel or JMP to complete it. If you are
using Excel, submit your answers in Excel, if you are using JMP, submit your output screenshots in
a Word File.
• If you submit multiple files, only the file with the latest time stamp would be graded.
• Label your work clearly.
Problem 1: Stock Market Performance.
The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are
used as measures of overall movement in the stock market. The DJIA is based on the price
movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say
the S&P 500 is a better measure of stock market performance because it is broader based. The
closing price for the DJIA and the S&P 500 for 15 weeks of a previous year follow (Barron’s web
site).
a) Develop a scatter chart for these data with DJIA as the independent variable. What does
the scatter chart indicate about the relationship between DJIA and S&P 500?
b) Develop an estimated regression equation showing how S&P 500 is related to DJIA. What
is the estimated regression model?
c) What is the 95% confidence interval for the regression parameter β1? Based on this
interval, what conclusion can you make about the hypotheses that the regression
parameter β1 is equal to zero?
d) What is the 95% confidence interval for the regression parameter β0? Based on this
interval, what conclusion can you make about the hypotheses that the regression
parameter β0 is equal to zero?
e) How much of the variation in the sample values of S&P 500 does the model estimated in
part (b) explain?
f) Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the
S&P 500.
g) Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value
in part (f) is beyond the range of the DJIA used to develop the estimated regression
equation?Problem 2: Estimating Fuel Mileage by Car Size.
The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and
trucks. A portion of the data for 311 compact, midsized, and large cars is given to you. 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.
a) Develop an estimated regression equation that can be used to predict the fuel efficiency
for highway driving given the engine’s displacement. Test for significance using the 0.05
level of significance. How much of the variation in the sample values of HwyMPG does
this estimated regression equation explain?
b) Create a scatter chart with HwyMPG on the y-axis and displacement on the x-axis for
which the points representing compact, midsize, and large automobiles are shown in
different shapes and/or colors. What does this chart suggest about the relationship
between the class of automobile (compact, midsize, and large) and HwyMPG?
c) Now consider the addition of the dummy variables ClassMidsize and ClassLarge to the
simple linear regression model in part (a). 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. Develop the estimated regression equation that can be used to predict the
fuel efficiency for highway driving, given the engine’s displacement and the dummy
variables ClassMidsize and ClassLarge. How much of the variation in the sample values of
HwyMPG is explained by this estimated regression equation?
d) Use significance level of 0.05 to determine whether the dummy variables added to the
model in part (c) are significant.
e) Consider the addition of the dummy variable FuelPremium, where the value of
FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. 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?
f) For the estimated regression equation developed in part (e), test for the significance of
the relationship between each of the independent variables and the dependent variable
using the 0.05 level of significance for each test.