Estimate the regression equation (Q) for the following demand data where the ind

Question

Estimate the regression equation (Q) for the following demand data where the independent variables are price (P) and consumer income (I). Also, test the statistical significance of the estimated parameters at the 5% level and show to what extent the independent variables can explain the variation in the quantities demanded.

Please provide step-by-step instructions on how to solve this in excel!

Qx Px I 2880 12.00 32,000 3600 8.00 31,500 3241 10.00 34,600 3420 8.00 33,160 3042 10.00 33,980 3600 8.00 35,610 3423 10.00 36,720 3600 8.00 38,000 3965 8.00 37,190 3786 8.00 39,890

Explanation / Answer

In excel go to DATA > DATA ANALYSIS >REGRESSION

IN Y-- select dependent variable quantity

X -Select both independent variables Price and quantity

following output is obtained

In the above table Since the p-value of the regression coefficient corresoinding to independent variable "price" is 0.003647 which is less than the level of significance 0.05.It indicates that the variable Price is significant.

In the above table Since the p-value of the regression coefficient corresoinding to independent variable "Index " is

0.101947 which is greater than the level of significance 0.05.It indicates that the variable "Index" is insignificant

From the above output since the value of the R-square i.e. coefficient of multiple determination is 0.829607 ,it indicates that 82.96 % of the variability in the response variable "QUANTITY" IS explained by tindependent variables "PRICE " and "INDEX"

SUMMARY OUTPUT Regression Statistics Multiple R 0.910827 R Square 0.829607 Adjusted R Square 0.780923 Standard Error 154.6061 Observations 10 ANOVA df SS MS F Significance F Regression 2 814648.9 407324.4 17.0407 0.002042 Residual 7 167321.2 23903.03 Total 9 981970.1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3612.554 940.3815 3.841583 0.006361 1388.905 5836.203 X Variable 1 -170.83 39.89671 -4.28181 0.003647 -265.171 -76.4895 X Variable 2 0.03915 0.020808 1.88146 0.101947 -0.01005 0.088353

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