econ103ps4answers

econ103ps4answers - Problem Set 4 Economics 103 Spring 2008...

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Problem Set 4 Economics 103 – Spring 2008 Prof. Ackerberg Due: Tuesday, May 27 at the beginning of class True/False – You must explain your answer for full credit. 1) If your regression suffers from “Imperfect Multicollinearity”, your estimated coefficients will be biased. False, “Imperfect Multicollinearity” does not cause bias. However, it can lead to imprecise estimates, i.e. high standard errors and large confidence intervals. 2) When testing hypotheses in a multiple regression model, you always need to use an F STAT . False, if you are testing a hypothesis regarding a single coefficient, you can use a t STAT . 3) Just because a coefficient is statistically significant does not mean that it is economically significant. True, “statistical significance” means that we can reject the null hypothesis that the coefficient equals zero. “Economic significance” means that the coefficient is large in an economic sense, i.e. that the effect is economically large. The two do not necessarily coincide – e.g. a coefficient can be statistically significant but not economically significant. We saw an example of this in class (Lecture note 11) 4) In a non-linear regression model, the effect of a change in X i on Y i varies depending on the level of X i . True, in a linear model, the effect of a unit change in X i (on Y i ) is constant, i.e. always the same. In a non-linear model this is not the case. For example, if Y i = 10 + 2 X i + 1 X i 2 , the effect of increasing X i from 1 to 2 is to increase Y i by 4. The effect of increasing X i from 2 to 3 is to increase Y i by 6. 5) The adjusted-R 2 always increases when you add an additional regressor variable to the regression. False, R 2 always increases when you add an additional regressor variable to the regression. Adjusted-R 2 does not always increase. If Adjusted-R 2 does increase, it tells us that the additional regressor has improved the fit of the model. If it does not increase, the additional regressor is not improving the fit of the model (and often we choose not to include the variable)
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6) In the following polynomial regression model Y i = 100 + 5.4 X i - 0.1 X i 2 the relationship between X i and Y i is concave (you can answer this either with or without calculus). True. Using Calculus, the derivative of this function is 5.4 – 0.2 X i , and the second derivative is -0.2. Since the second derivative is negative, the function is concave. One can also do this by plugging in various values of X i . When X i = 1, Y i = 105.3, when X i = 2, Y i = 110.4, and when X i = 3, Y i = 115.3. Since the effect of increasing X i by one unit decreases as X i increases, the function is concave (you could also plot these points and see that the function looks concave (the function looks like a cave when viewed from below). Longer Answer:
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This note was uploaded on 03/10/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.

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econ103ps4answers - Problem Set 4 Economics 103 Spring 2008...

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