Question

2. Using the following regression summery output for the estimation of demand for a product. 9691 Regression Statistics R Square 0.969 dr SS F Significance F Regression 3 3656.960437 318.144172 0.00000000 Residual 31 118.7781973 Total 34 3775.7386351 Coefficients Stat P-value Intercept 87.30|24.15250613 0.00000000 Price (Px) -0.80 -10.19361420.00000000 Price Other (Py) -0.60 3.263427775|0.01580374 Income (1) 1.006.097885873 0.00000985 a. Comment on the significance of the regression model as a whole: point b. Comment on the significance of the specific coefficients: 1 points C. Interpret the R' value: points d. State the estimated demand function (Q is a linear function of P P, and I): point e. Determine the change in Qx if Px increases by Sl: points f.fp. - 567.50, P. - $50.5, 1 - 569, compute the value for point

Answer 1

a. The F-statistic for the regression model is 318.144172.
The F-critical value at F.001,3,31 is approximately 7. Since 318 > 7, we reject the null hypothesis of no overall significance of the model. It means, the regression model is significant as a whole.

b. The p-value of Price (Px) is very low (i.e. 0.000), therefore it is signficant.
The p-value of Other Price (Py) is 0.015, which means it is significant but only till 98.5% (=100-1.5). It is not significant at, say 99%.
The p-value of Income (I), again, is very low. Therefore, it is significant.

c. The R-squared of the model is 0.969 or 96.9%. It means that the independent variables explain 96.9% variation in the average value o the dependent variable, while the rest 3.1% is not explained by the model and is the error term component.
Therefore, the everage demand for a product is 96.9% affected by its price, other price, and income level. The rest is affected by some other factors not included in the model.

d. Qx = 87.30 - 0.80Px - 0.60Py + I