ECO 351 - Business Statistics II - Problem Set 2

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2nd Problem Set from my ECO 351 Business Statistics II course at UNC Greensboro.

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2. (Studenmund, exercise 1.5) Suppose you collect data on the heights and weights of 30 randomly selected men and estimate the following regression equation: 2(a). The coefficients in the new equation are not the same as those estimated in the previous equation because the sample is different. When the sample changes, so too can the estimated coeffcients. 2(b). Equation 1.21 has the steeper slope (6.38 > 4.30) while Equation 1.24 has the greater intercept (125.1 > 103.4). 2(c). We use the equation ^ Yi = 125:1 + 4:03Xi to generate predictions and calculate the residuals as ei = Yi
3. (Studenmund, exercise 1.6) Consider the following estimated regression equation: 3(a). The coefficient of Li represents the change in the percentage chance of making a putt when the length of the putt increases by 1 foot. In this case, the percentage change of making a put decreases by 4.1 for each foot longer the putt is. 3(b). The predicted chance is ^ Pi = 83:6
4. (Studenmund, exercise 1.9) Your friend has an on-campus job making telephone calls to alumni asking for donations to your college’s annual fund, and she wonders whether her calling is making any difference. In an attempt to measure the impact of student calls on fund raising, she collects data from 50 alums and estimates the following equation: 4(a). 2.39 is the estimated constant term, and it is an estimate of the gift when the alum has no income and no calls were made to that alum. 0.001 is an estimate of the slope coefficient of INCOME, and it tells us how much the gift would be likely to increase when the alum’s income increases by a dollar, holding constant the number of calls to that alum. 4.62 is an estimate of the slope coefficient of CALLS, and it tells us how much the gift would be likely to increase if the college made one more call to the alum, holding constant the alum’s income. The signs of the estimated slope coefficients are as expected, but we typically do not develop hypotheses involving constant terms. 4(b). The linear function provides predicted or …tted values, so the left-hand side of the equation should be ^G i instead of Gi. The actual donations Gi can be decomposed, after estimating the regression model, as a predicted part and the regression residual: Gi = ^Gi+ei.
4. (Studenmund, exercise 1.9) Your friend has an on-campus job making telephone calls to alumni asking for donations to your college’s annual fund, and she wonders whether her calling is making any difference. In an attempt to measure the impact of student calls on fund raising, she collects data from 50 alums and estimates the following equation: 4(c). This is not a mistake. The stochastic error term ("i) is not observed and does not show up in the equation that generates predictions ^Gi (otherwise, we wouldn’t be able to predict at all). 4(d). A change in scale does not change the predicted values. If a $1 increase in income increases expected donations by $0.001, then a $1,000 increase in income will increase ex-pected donations by $1. If income is measured in $1,000, then its coefficient will be 1. All other coefficients remain unchanged, so that ^Gi = 2:39 + 1.0Ii + 4.62Ci
5. The distinction between the stochastic error term and the residual is one of the most difficult concepts to master. In your own words, define the error term and define the residual. In what ways (state at least 2) do the residual and error term differ? 5. The error term "i is the difference between the dependent variable Yi and the population regression function. The residual is the difference between the dependent variable Yi and the estimated regression function. The differences between the two are: (1) "i is not observed, whereas ei is estimated; (2) "i is a quantity in the population, whereas ei is calculated in the sample; (3) "i is the difference between Yi and the unobserved population regression function, whereas ei is the difference between Yi and the estimated regression function.
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