Please help me with this question, show solutions! You have been hired by the Ti

Question

Please help me with this question, show solutions!

You have been hired by the Tim Hortons restaurant group to analyze the gross sales volume at their chain restaurants. You believe this is a function of various variables of the restaurants’ location and collect the data one these.

You have: • Yi = Customers, i.e., check volume at restaurant i • Ni = Number of competitive restaurants nearby restaurant i • Pi = Population nearby restaurant i • Ii = Average household income nearby. The first regression you estimate (i.e., “run”) includes all these variables and gives you the following results, with standard errors reported in the parenthesis below the coefficients. Yˆ i = 102192 9075 (2053) Ni + 0.3547 (0.0727) Pi + 1.288 (0.543) Ii R¯2 = 0.579 n = 33

After looking at your regression results, the fat cats at Tim’s, who only care about income and have no training in econometrics, don’t see why you would want the population (Pi) variable in the regression.

Thus, you drop the population variable from the regression and show them the new estimate. Yˆ i = 84439 1487 (1778) Ni + 2.322 (0.664) Ii R¯2 = 0.258 n = 33

(a) Carefully and fully compare the two regression results. Calculate the t-stats for all estimated coefficients.

(b) What are the biggest differences and why do you think this happened? Briefly comment.

Explanation / Answer

in the first model there are there indpendent variables N, P and l and

Yˆ i = 102192 9075 (2053) Ni + 0.3547 (0.0727) Pi + 1.288 (0.543)

all the independent variables are significant at 5% confidence interval

Yˆ i = 84439 1487 (1778) Ni + 2.322 (0.664) Ii R¯2 = 0.258 ,n = 33

model first is better as all the variable are significant at 5% level of significance and also R2 is more

(b) it is due to the variable P is removed from the model inspite of that the this variable is signifiant

variable N P l coeff 9075 0.3547 1.288 SE(coeff) 2053 0.0727 0.543 t 4.420360448 4.878954608 2.372007366

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