47 - Chapter 3, Exercise Solutions, Principles of...

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Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 47 EXERCISE 3.10 (a) The coefficient 2 β represents the increase in price from an extra square foot of living area. We can refer to it as the marginal price per square foot. (i) A 95% interval estimate of 2 β for all houses is: 2 (0.975,1078) 2 se( ) bt b ±× = 92.747 ± 1.962 × 2.4105 = (88.02, 97.48) We estimate, with 95% confidence, that the marginal price per square foot for all houses lies between $88.02 and $97.48. (ii) A 95% interval estimate of 2 β for town houses is: 2 (0.975,68) 2 se( ) b = 55.585 ± 1.995 × 7.0999 = (41.42, 69.75) We estimate, with 95% confidence, that the marginal price per square foot for town houses lies between $41.42 and $69.75. (iii) A 95% interval estimate of 2 β for French style houses is: 2 (0.975,95) 2 se( ) b = 184.167 ± 1.985 × 10.1626 = (163.99, 204.34) We estimate, with 95% confidence, that the marginal price per square foot for French style houses lies between $163.99 and $204.34. These confidence interval estimates tell us that town houses have a lower marginal price per square foot compared to the average, and also that French style houses have a much higher marginal price per square foot than all houses. Furthermore, we see that the
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