Ch 4 nd 5 extra probs answers

Ch 4 nd 5 extra probs answers - Econ 120B Solutions to...

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Econ 120B Solutions to Chapters 4 and 5 Practice Problems 1. a. For every one inch increase in the average height of their parents, the student’s height increases, on average, by 0.73 of an inch. There is no reasonable interpretation for the intercept (the average height of a student whose parents have an average height of zero!). b. 45 percent of the variation in the height of students can be explained by the model, i.e., can be explained by the average height of the parents. The SER is a measure of the spread of the observations around the regression line. The magnitude of the typical deviation from the regression line or the typical regression error here is two inches. c. 19.6 + 0.73 × 70.06 = 70.74. d. Tall parents will have, on average, tall children, but they will not be as tall as their parents. Short parents will have short children, although on average, they will be somewhat taller than their parents. e. 0 : 1 0 = β H , t =7.30, for 0 : 1 1 > H , the critical value for a two-sided alternative is 1.645. Hence we reject the null hypothesis. f. For the simple linear regression model, 0 : 1 0 = H implies that = 0. Hence it is the same test as in (e). 2 R g. 0 : 0 0 = H , t =2.72, for 0 : 0 1 H , the critical value for a two-sided alternative is 2.58. Hence we reject the null hypothesis in (i). For the slope we have 1 : 1 0 = H , t =-2.70, for 1 : 1 1 H , the critical value for a two-sided alternative is 1.96. Hence we reject the null hypothesis in (ii). h. (0.73x5 – 1.96 × 0.10x5, 0.73x5 + 1.96 × 0.10x5) = (0.53x5, 0.93x5) = (2.65, 4.65) i. This is an example of mean reversion. Since the aristocracy was, on average, taller, he was concerned that their children would be shorter and resemble more the rest of the population. If this conclusion were true, then eventually everyone would be of the same height. However, we have not observed a decrease in the variance in height over time. 2. a. Interpretation of slope coefficient: A relative increase in the population rate of one percentage point, from 0.01 to 0.02, say, lowers relative per-capita income by almost 20 percentage points (0.188), on average. This is a quantitatively important and large effect. Interpretation of the intercept: Nations which have the same population growth rate as the United States have, on average, roughly half as much per capita income. Around 52% of the variation in relative per capita income can be explained by the variations in the relative population growth rate. The magnitude of a typical deviation from the regression line is about 0.2 (20 percentage points). The t -statistic is 5.93, making the relationship statistically significant, i.e., we can reject the null hypothesis that the slope is different from zero. b.
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Ch 4 nd 5 extra probs answers - Econ 120B Solutions to...

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