Question

4. Given the following information on the number of weekly taxi customers in 10 cities, run a regression in Excel (with number of weekly taxi customers as the dependent variable) and answer the following questions. What do the signs of the estimated coefficients imply? Which of the parameters are significant at the 5 percent level? CHAPTER 5 Demand Estimation 221 Number of weekly taxl customers Price per mile Population of a city Monthly income of customers Average parking rates per month 500 1,000,000 133.000 485.000 350,000 78000 1.500.000 35,000 213,000 437,000 535,000 7,000,000 550.000 1.250.000 90,000 450.0XXO 9.OXXOXO 170,000 650XXO MAXX 025.000 50.000 30,000 40.000 35.000 55.000 45,000 35,000 30,000 25.000 20.000

Answer 1

The multiple regression analysis is done for the given data.

Here,

• No. of weekly taxi customers is the dependent variable,
• price per mile, population of a city, monthly income of customers and Average parking rates per month are explanatory variables.
• All assumptions of classical regression model holds good.

Given below is the regression data done in excel and the results are shown here.

SUMMARY OUTPUT
	Regression Statistics
Multiple R		0.985414531
R Square		0.971041798
Adjusted R Square		0.942083595
Standard Error		48685.31013
Observations		9
ANOVA
		df	SS	MS	F	Significance F
Regression		4	3.17923E+11	79480796133	33.5325304	0.002467165
Residual		4	9481037689	2370259422
Total		8	3.27404E+11
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept		1224802.778	94625.98345	12.94362007	0.000205514	962078.9297	1487526.627
Price per mile		-321038.3876	38130.33821	-8.419500132	0.001089502	-426905.1785	-215171.5967
Population of city		0.119149203	0.043779052	2.721603125	0.052899234	-0.00240093	0.240699337
Monthly income of   customers		-2.412934067	1.903461003	-1.267656161	0.273690238	-7.697789052	2.871920918
Average parking rates per month		-3052.840707	814.067561	-3.750107305	0.019945222	-5313.054602	-792.626812

From the above table it can be seen that -

The coefficients of Price per mile, Average parking rates per month and Monthly income of customers are negative. it means that the there is an inverse relationship between the dependent variable (No. of weekly taxi customers) and the above mentioned variables, i.e. if any of such explanatory variables increases in values it will reduce the value of dependent variable.

Further population of the city is directly proportional to no. of taxi customers as the coefficeint is positive.(see table).

To find which parameters are statistically significant we have to look at p-values. At 5% alpha, if p-value is <0.05 it means it is statistically significant.

So from the above table we can see that the values of parameters Average parking rates per month and Price per mile are <0.05. So these are statistically significant at 5% level.