BUS 771 Unit 7 Homework 1. 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...

1 answer below »

BUS 771



Unit 7 Homework


1. 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 contained in the file fueldata.xlsx which you can download from the class D2L shell. The dataset contains the following variables:


Class identifies the size of the car; Compact, Midsize, or Large


Displacement = engine displacement in liters


FuelType shows whether the car uses premium (P) or regular (R) fuel


HwyMPG = fuel efficiency rating for highway driving in miles per gallon


a. Develop an estimated regression equation to predict the fuel efficiency for highway driving given the engine’s displacement. Plot the residuals from this regression to see if you see any pattern. Conduct a hypothesis test to determine whether the coefficient on Displacement is statistically significantly different from 0 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. Add 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. Estimate the new regression equation. What happened to the adjusted R2
when these variables were added to the regression? What does this tell you?


d. Use significance level of 0.05 to determine whether the dummy variables added to the model in part c are significant.


e. Finally add the dummy variable FuelPremium, (which is 1 if the car uses premium fuel and 0 if the car uses regular fuel) to the regression. What happened to the adjusted R2
when these variables were added to the regression? What does this tell you?


f. For the estimated regression equation developed in part e, test for the significance of the overall regression relationship (using the F-statistic) and for each of the independent variables the 0.05 level of significance for each test.


Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).


2. Return to the ‘cars.xlsx’ dataset that was used in the Unit 6 Homework. Recall that this dataset includes data on the 0-60 time (TIME), top speed (SPEED), curb weight (WEIGHT), and horsepower (HP) of 30 automobiles.



There are good reasons based in physics to believe that the relationship between horsepower and 0-60 time is non-linear. Look again at the scatter plot of HP (x-axis) and 0-60 time (y-axis) from the Unit 6 Homework. To test the goodness of fit of one possible non-linear relationship estimate the following quadratic regression: TIMEi
= β0
+ β1HPi
+ β2HPi
2
+ ε Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).



Compare the results from this regression to those from the Unit 6 Homework. Which do you prefer and why?



3. Use the "BEER" data set to answer the following question. (Also on the course D2L site). The data set includes 30 observations on beer consumption and related data. The variables included are as follows:




q = quantity of beer purchased (in liters)



pB = price of beer (in dollars)



pL = price of other liquor (in dollars)



pR = price of remaining (non-alcoholic) goods & services (in dollars)



m = income (in dollars)



a. What sign do you expect for each coefficient and why?


b. Estimate a regression to explain the quantity of beer purchased as a function of the price, price of liquor, price of remaining goods, and income. Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).


c. Interpret the parameters.


d. Are any of the regressors individually significant in explaining the quantity of beer purchased? If so, at what level?


e. Suppose that beer industry representatives hypothesize that the marginal propensity to buy beer out of an additional dollar of income is $0.01. Conduct a hypothesis test to determine if there is any validity to their conjecture. Use a = 1%.


f. Conduct a hypothesis test to determine if the regressors are jointly significant in explaining the quantity of beer purchased. Be sure to state the null and alternative hypotheses formally.

Answered Same DayJul 15, 2021

Answer To: BUS 771 Unit 7 Homework 1. The U.S. Department of Energy’s Fuel Economy Guide provides fuel...

Pooja answered on Jul 16 2021
130 Votes
data&otput
    obs    q    pB    pL    pR    m        SUMMARY OUTPUT
    1    81.7    1.78    6.95    1.11    25088
    2    56.9    2.27    7.32    0.67    26561        Regression Statistics
    3    64.1    2.21    6.96    0.83    25510        Multiple R    0.906707056
    4    
65.4    2.15    7.18    0.75    27158        R Square    0.8221176855
    5    64.1    2.26    7.46    1.06    27162        Adjusted R Square    0.7936565151
    6    58.1    2.49    7.47    1.1    27583        Standard Error    3.5692189896
    7    61.7    2.52    7.88    1.09    28235        Observations    30
    8    65.3    2.46    7.88    1.18    29413
    9    57.8    2.54    7.97    0.88    28713        ANOVA
    10    63.5    2.72    7.96    1.3    30000            df    SS    MS    F    Significance F
    11    65.9    2.6    8.09    1.17    30533        Regression    4    1471.9315617683    367.9828904421    28.8855895951    0.0000000048
    12    48.3    2.87    8.24    0.94    30373        Residual    25    318.4831048983    12.7393241959
    13    55.6    3    7.96    0.91    31107        Total    29    1790.4146666667
    14    47.9    3.23    8.34    1.1    31126
    15    57    3.11    8.1    1.5    32506            Coefficients    Standard Error    t Stat    P-value    Lower 95%    Upper 95%    Lower 95.0%    Upper 95.0%
    16    51.6    3.11    8.43    1.17    32408        Intercept    82.1587081375    17.961759844    4.5740901143    0.0001123899    45.1657712635    119.1516450116    45.1657712635    119.1516450116
    17    54.2    3.09    8.72    1.18    33423        pB    -23.7426002252    5.4294091862    -4.3729620316    0.000189267    -34.9246777629    -12.5605226876    -34.9246777629    -12.5605226876
    18    51.7    3.34    8.87    1.37    33904        pL    -4.077409697    3.8904890729    -1.0480455338    0.3046447426    -12.0900219317    3.9352025376    -12.0900219317    3.9352025376
    19    55.9    3.31    8.82    1.52    34528        pR    12.9243403319    4.1638956166    3.1039059386    0.0046977654    4.3486367799    21.5000438839    4.3486367799    21.5000438839
    20    52.1    3.42    8.59    1.15    36019        m    0.0019945593    0.0007759082    2.5706124445    0.016492276    0.0003965464    0.0035925721    0.0003965464    0.0035925721
    21    52.5    3.61    8.83    1.39    34807
    22    44.3    3.55    8.86    1.6    35943
    23    57.7    3.72    8.97    1.73    37323
    24    51.6    3.72    9.13    1.35    36682        RESIDUAL OUTPUT                PROBABILITY OUTPUT
    25    53.8    3.7    8.98    1.37    38054
    26    50    3.81    9.25    1.41    36707        Observation    Predicted...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here