Question

Given the data in Table A, develop a multivariate regression analysis of the relationship between Product Demand and the other variables in the table (Average Customer Income, Number of Snow Days in Season, and the Average Gasoline Price).Do the results of your analysis confirm your expectations and do they make economic sense?

Regression Statistics
Multiple R	0.999999903
R Square	0.999999805
Adjusted R Square	0.999999799
Standard Error	1.031348397
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	3	523836040.9	1.75E+08	1.64E+08	0
Residual	96	102.1132335	1.06368
Total	99	523836143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	35001.37051	0.998051161	35069.72	0	34999.38939	35003.35	34999.38939	35003.35
Average Customer Income	0.157489612	7.10596E-06	22163.02	0	0.157475507	0.157504	0.157475507	0.157504
Number of Snow Days In Season	23.64406609	0.007643789	3093.239	9.5E-242	23.62889329	23.65924	23.62889329	23.65924
Average Gasoline Price ($/gallon)	-3.866980648	0.294996586	-13.1086	4.12E-23	-4.452544243	-3.28142	-4.452544243	-3.28142

Answer 1

we know that multivariate equation for 3 independent variables is given as

y = a + bx + cy + dz

where a is intercept, b is slope coefficient for x, c is slope coefficient for y and d is slope coefficient for z

x is average customer income, y is number of snow days in season and z is average gasoline price

setting the value from the data table

we can write

y = 35001.3705 + 0.1574(Average customer income)+23.6441(number of snow days in season)-3.8670(average gasoline price)

(each coefficient value is rounded to 4 decimals)

Yes, it confirms out expectations because equation is showing logical data for each variable. For example, product is required more in snow days, so the coefficient of snow day is very high. Each one of the variables are significant.