SUMMARY OUTPUT LINEAR SPECIFICATION Regression Statistics Multiple R 0.83756222

Question

SUMMARY OUTPUT                        LINEAR SPECIFICATION       

Regression Statistics    

Multiple R                        0.83756222     

R Square                          0.70151047    

Adjusted R Square         0.62191327     

Standard Error                              1618.81215    

Observations                  20            

ANOVA      

                         df                     SS                       MS                    F                           Significance F

Regression             4        92382398.01        2E+07         8.8133                         0.00072216

Residual                15        39308291.79         3E+06  

Total                     19        131690689.8                

Coefficients       Standard Error t Stat    P-value                             Lower 95%         Upper 95%

Intercept           21395.2217       8496.079221      2.518    0.0236               3286.24641        39504.1971

Price                    -7583.4231         2063.676471      -3.675 0.0023                -11982.0481        -3184.7981

Income                              0.17754317        0.35915738        0.494 0.6282               -0.58798314      0.94306947

Pmovies              -148.95038         860.5426988      -0.173 0.8649                 -1983.15486        1685.25409

Nshows              868.719576        301.5288353      2.881    0.0114               226.025682        1511.41347                    

SUMMARY OUTPUT      LOG-LINEAR SPECIFICATION         

Regression Statistics     

Multiple R                         0.83216727    

R Square                          0.69250237     

Adjusted R Square          0.610503     

Standard Error                0.10154781   

Observations                  20            

ANOVA       

                                           df          SS                                      MS           F                          Significance F

Regression                       4            0.348346806                    0.087    8.4452               0.00089283

Residual                            15          0.154679352                    0.01   

Total                                  19          0.503026157                

                             Coefficients       Standard Error   t Stat     P-value             Lower 95%         Upper 95%

Intercept            5.40118406       5.641522633      0.957    0.3535                -6.62344418        17.4258123

lnP                       -1.6443489         0.489743922     -3.358   0.0043               -2.688214            -0.6004838

lnM                      0.28830645       0.677469767     0.426     0.6765               -1.15568706        1.73229997

lnPmov               -0.0889847        0.294114327      -0.303     0.7664              -0.71587496        0.5379055

lnNshows           1.18395497        0.410078457      2.887        0.0113               0.30989289        2.05801705

5. (32 points total) Provided above are the results of two regressions in which the number of bags of popcorn sold in a Midwestern town in a week is analyzed using the data on the price of popcorn (Price P), average household income (Income M), average price of a movie ticket (Pmovie), and the number of movie shows (Nshows).

(4 points) Which of the two regressions provides a better overall fit, linear or log-linear? Explain what makes you think so.

b. (6 points) Use the regression output to write two alternative equations for demand for popcorn  

QD =   

lnQD =   

c. (6 points) Use the results of the log-linear regression to determine the income elasticity of demand for popcorn. Show your work. According to your findings, is popcorn a normal or an inferior good?           

d. (6 points) Currently, the price of a popcorn bag is $2, the average household income is $30,030, the average price of a is $6, and 12,700 bags of popcorn are sold weekly. Use the results of the linear regression to determine the own price elasticity of demand for popcorn at the current price. Once again, show your work. Is the demand for popcorn price elastic or price inelastic at P=$2?             

e. (6 points) Under the current circumstances, what price would maximize revenues from popcorn sales? Explain what makes you think so.          

f. (4 points) Which of the independent variables used in the regression has the least effect on the consumption of popcorn? How can you tell?      

This is a practice exam. I had someone answer it before but they only answered half the questions with no explanations.  

Explanation / Answer

1) I think both the models provides equal measure of goodness of fit. I based my answer on the value of R-square of both the models. R-square explains the percentage of variation in dependent variable that is explained by independent variable. As R-square value of both the models are almost indentical, both regression models provide almost equal goodness of fit.

2) Based on linear regression

QD=21395.22 -7583 P + 0.1775 M -148.95 Pmovies + 868.72 Nshows

Based on log linear regression

ln QD= 5.4011-1.64 lnP + 0.288 lnM -0.088 lnPmovies + 1.1839 ln Nshows

3) Income elasticity of demand = change in quantity demanded/ change in income level c c

= first derivative of ln Qd

1/QD= 0.288/M

QD= 3.472 M

Here, as income elasticity of demand is positive, the popcorn is a normal good

f) From linear model,income and Pmovies independent variable used in regression has the least effect on consumption as Pvalues for these variable are higher than 5%. Hence, we fail to reject the null hypothesis which states that this variable has no significant impact on dependent variable.

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