Use the below table to answer the following. The data set includes 30 observatio
ID: 3263103 • Letter: U
Question
Use the below table to answer the following. 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.
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.
obs q pB pL pR m 1 81.7 1.78 6.95 1.11 25088 2 56.9 2.27 7.32 0.67 26561 3 64.1 2.21 6.96 0.83 25510 4 65.4 2.15 7.18 0.75 27158 5 64.1 2.26 7.46 1.06 27162 6 58.1 2.49 7.47 1.1 27583 7 61.7 2.52 7.88 1.09 28235 8 65.3 2.46 7.88 1.18 29413 9 57.8 2.54 7.97 0.88 28713 10 63.5 2.72 7.96 1.3 30000 11 65.9 2.6 8.09 1.17 30533 12 48.3 2.87 8.24 0.94 30373 13 55.6 3 7.96 0.91 31107 14 47.9 3.23 8.34 1.1 31126 15 57 3.11 8.1 1.5 32506 16 51.6 3.11 8.43 1.17 32408 17 54.2 3.09 8.72 1.18 33423 18 51.7 3.34 8.87 1.37 33904 19 55.9 3.31 8.82 1.52 34528 20 52.1 3.42 8.59 1.15 36019 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 25 53.8 3.7 8.98 1.37 38054 26 50 3.81 9.25 1.41 36707 27 46.3 3.86 9.33 1.62 38411 28 46.8 3.99 9.47 1.69 38823 29 51.7 3.89 9.49 1.71 38361 30 49.9 4.07 9.52 1.69 41593Explanation / Answer
b) q = 82.1587 -23.7426 *pB -4.0774096 *pL +12.92434033*pR +0.001994559*m
c) the coefficient of parameter are change in q when independent variable changes by 1 unit
d)
if p-value is less than level of significance , then the variable is significant
here all variable are significant except pL as their p-value < 0.05
e)
ts = (0.01 -0.001994559)/0.000775908 = 10.3175
this is more than critical value
hence there is no significant evidence that he marginal propensity to buy beer out of an additional dollar of income is $0.01
f) p-value for F is 4.77*10^(-9) << 0.01
hence the overall model is significant
SUMMARY OUTPUT Regression Statistics Multiple R 0.906707056 R Square 0.822117685 Adjusted R Square 0.793656515 Standard Error 3.56921899 Observations 30 ANOVA df SS MS F Significance F Regression 4 1471.931562 367.9828904 28.8855896 4.77E-09 Residual 25 318.4831049 12.7393242 Total 29 1790.414667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 82.15870814 17.96175984 4.574090114 0.00011239 45.16577 119.1516 45.16577 119.1516 pB -23.74260023 5.429409186 -4.37296203 0.00018927 -34.9247 -12.5605 -34.9247 -12.5605 pL -4.077409697 3.890489073 -1.04804553 0.30464474 -12.09 3.935203 -12.09 3.935203 pR 12.92434033 4.163895617 3.103905939 0.00469777 4.348637 21.50004 4.348637 21.50004 m 0.001994559 0.000775908 2.570612445 0.01649228 0.000397 0.003593 0.000397 0.003593Related Questions
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