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Homework answers / question archive / Question Three {10 Marks From the following is the regression output of the quantity demanded of a commodity (Y), its price (X1) and consumer income (X2) from 1986 to 2005 (10 Marks) SUMMARY OUTPUT Regression Statistics Multiple R 0
Question Three {10 Marks From the following is the regression output of the quantity demanded of a commodity (Y), its price (X1) and consumer income (X2) from 1986 to 2005 (10 Marks) SUMMARY OUTPUT Regression Statistics Multiple R 0.98398 R Square 0.968217 Adjusted R Square 0.964478 Standard Error 7.204988 Observations 20 ANOVA df Regression Residual Total SS MS F gnificance F 2 26884.3 13442.15 258.9418 1.86E-13 17 882.5015 51.91185 19 27766.8 Intercept X1 X2 Coefficientsandard Err Stat P-value Lower 9596Upper 95%ower 95.Opper 95.0% 114.0738 29.93119 3.811201 0.001396 50.9245 177.2231 50.9245 177.2231 -9.47019 1.819581 -5.2046 7.16E-05 -13.3092 -5.63121 -13.3092 -5.63121 0.028937 0.006422 4.505861 0.000312 0.015387 0.042486 0.015387 0.042486 a. What is the interpretation of the coefficients on price (X1), and consumer income (X2); (4 Marks) b. Determine the commodity Y's quantity demanded and demand curve when price is $4; income is $3000. Show the demand curve when price is expressed as a function of quantity. (6 Marks)
a. The coefficients are as you would expect according to economic theory. There is a negative relationship between the price of the good and its demand (X1, -9.47019), and a positive relationship between income and demand (X2, 0.028937). The coefficients are also statistically significant since the absolute values of their t-stats are fairly high. This points to the good being a normal good.
b. Y = 114.0738 - 9.47019X1 + 0.028937X2, if X1 = 4, X2 = 3000
Y = 114.0738-9.47019*4+0.028937*3000 = 163.004, is the quantity demanded
We can plot the demand schedule for income = 3000 as follows:
| P | Q=114.0738-9.47019*X1+0.028937*3000 |
| 1 | 191.41461 |
| 2 | 181.94442 |
| 3 | 172.47423 |
| 4 | 163.00404 |
| 5 | 153.53385 |
| 6 | 144.06366 |
| 7 | 134.59347 |
| 8 | 125.12328 |
| 9 | 115.65309 |
| 10 | 106.1829 |
| 11 | 96.71271 |
Price on vertical axis and quantity on horizontal axis.
