Question

File b--9 구제 -50 Part Five (answer all parts) 0-1200-50P+1 30) (o9 +00Y+e. (001) You are presented with the following regression eo R2 945,n 44 Q-quantity of Coca-Cola demanded P price of Coca-Cola ps = price of Pepsi-Cola Y = consumer income (a)Do the signs of the estimated coefficients correspond with thé theory of demand? (b) Which of the estimated coefficients are significant at alpka Vos? Which are significant at alpha 005 (e) What can you say about the economic significance of the variables P, p, and Y (d) Calculate adjusted R2 (e) Would you expect the F-test to show that theoverall model has a statistically significant fit Explain. c ? I of 1 Words 126 us a Part Five (answer all parts) You are presented with the following regression equation 1200-50 P+1p +005 Y + e. (30) (04) (001) R2 945,n-44 o quantity of Coca-Cola demanded P price of Coca Cola pprice of Pepsi Cola Y consumer income (a) Do the signs of the estimated coefficients correspond with the theory of demand (b)Which of the estimated coefficients are significant at alpha 05? Which are sinificant at alpha 0057 (e) What can you say about the economic significance of the variables P, P, and Y? (d) Calculate adjusted R (c) Would you expect the F-test to show that the overall model has a statistically sinificant ft Explain

Answer 1

Ans 1)

Q=1200-50P+1P*+0.005Y+e

We can see that coefficient of price of Coca-Cola is negative that is as per the theory of demand because if Price of Coca-Cola increases by $1 that will decrease the demand for Coca cola by 50 units assuming all other things fixed.

Coefficient of price of Pepsi-Cola is negative in sign because if Price of Pepsi Cola increase it will decrease the demand for Pepsi Cola and increase the demand of Coca Cola due to substitution effect

Hence all the signs of the estimated coefficients are as per the theory of demand.

Ans 2)

Assuming that values in parantheses are standard error

Formula for t-statistic= Coefficient Value/SE(Coefficient)

t-statistic of Price of Coca-Cola coefficient=50/30=1.667
t-statistic of Price of Pepsi-Cola coefficient=0.1/0.04=2.5
t-statistic of Income=0.005/0.001=5

At significance level 0.05 and df=sample size-1=44-1=43

Critical t value at (0.05,43)=1.645

Hence we can reject the null hypothesis for all the variables as calculated t value> critical t statistic

At significance level 0.005 and df=sample size-1=44-1=43

Critical t value at (0.005,43)=2.576

Hence we can not reject the null hypothesis except for Income as calculated t value< critical t statistic whereas Calculated t statistic > Critical t statistic.

Ans 3)

At alpha=0.05 P, P* and Y are statistically significant than zero hence these variables affect the quantity demanded of Coca Cola

AT alpha =0.005 only Y variable is statistically significant than zero where other variables are not statistically different than zero

Therefore at alpha=0.005 only Y affects the quantity demanded for Coca-Cola not P, P*

Ans 4)

Formula for adjusted R^2=1-(1-R^2)(N-1)(1/(N-p-1)

N=44, p=3 (P,P*,Y), R^2=0.945

1-(1-0.945)(43)(1/(44-3-1)=1-(0.005)(43/40)=0.994625