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Given the data in Table A, develop a multivariate regression analysis of the relationship between Product...

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). 1. What are the findings of your analysis? Please explain what they mean and provide all necessary tables and other related information that is the result of your analysis

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
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

we know that multivariate equation for independent variables is given as

y = A + Bx + Cy + Dz

where A is intercept of equation, B is slope for x, C is slope for y and D is slope for z

Using the given 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)

Finding of analysis are

(A) slope for each independent variable as well as for intercept are significant at 0.05 level of significance

(B) Overall ANOVA result is significant because the p value corresponding to F statstic is less than 0.05 significance level.

(C) Coefficient of determination (R square) value is 0.9999, which means that the 99.99% variation in the dependent variable is explained by the regression equation given above.

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