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PS 6 - solutions - ECON 120B SOLUTION KEY TO HW 6 Exercise...

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ECON 120B SOLUTION KEY TO HW 6 Exercise 8.1 (a) The percentage increase in sales is 198 196 196 100 1.0204%. - × = The approximation is 100 × [ln (198) - ln (196)] = 1.0152%. (b) When Sales 2002 = 205, the percentage increase is - × = 205 196 196 100 4.5918% and the approximation is 100 × [ln (205) - ln (196)] = 4.4895%. When Sales 2002 = 250, the percentage increase is 250 196 196 100 27.551% - × = and the approximation is 100 × [ln (250) - ln (196)] = 24.335%. When Sales 2002 = 500, the percentage increase is 500 196 196 100 155.1% - × = and the approximation is 100 × [ln (500) - ln (196)] = 93.649%. (c) The approximation works well when the change is small. The quality of the approximation deteriorates as the percentage change increases. Exercise 8.2 (a) According to the regression results in column (1), the house price is expected to increase by 21% ( = 100% × 0.00042 × 500 ) with an additional 500 square feet and other factors held constant. The 95% confidence interval for the percentage change is 100% × 500 × (0.00042 ± 1.96 × 0.000038) = [17.276% to 24.724%]. (b) Because the regressions in columns (1) and (2) have the same dependent variable, 2 R can be used to compare the fit of these two regressions. The log-log regression in column (2) has the higher 2 , R so it is better so use ln( Size ) to explain house prices. (c) The house price is expected to increase by 7.1% ( = 100% × 0.071 × 1). The 95% confidence interval for this effect is 100% × (0.071 ± 1.96 × 0.034) = [0.436% to 13.764%]. (d) The house price is expected to increase by 0.36% (100% × 0.0036 × 1 = 0.36%) with an additional bedroom while other factors are held constant. The effect is not statistically significant at a 5% significance level: = = < 0.0036 0.037 | | 0.09730 1.96. t Note that this coefficient measures the effect of an additional bedroom holding the size of the house constant.
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