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Unformatted text preview: Instructor : H.H. Kim 1 Econometrics Quiz 03 Name: ______________________ 1) You have been asked by your younger sister to help her with a science fair project. During the previous years she already studied why objects float and there also was the inevitable volcano project. Having learned regression techniques recently, you suggest that she investigate the weight‐
height relationship of 4th to 6th graders. Her presentation topic will be to explain how people at carnivals predict weight. You collect data for roughly 100 boys and girls between the ages of nine and twelve and estimate for her the following relationship: = 45.59 + 4.32 × Height4, R2 = 0.55, SER = 15.69 (3.81) (0.46) where Weight is in pounds, and Height4 is inches above 4 feet. (a) Interpret the results. (b) You remember from the medical literature that females in the adult population are, on average, shorter than males and weigh less. You also seem to have heard that females, controlling for height, are supposed to weigh less than males. To see if this relationship holds for children, you add a binary variable (DFY) that takes on the value one for girls and is zero otherwise. You estimate the following regression function: = 36.27 + 17.33 × DFY + 5.32 × Height4 – 1.83 × (DFY × Height4), (5.99) (7.36) (0.80) (0.90) R2 = 0.58, SER = 15.41 Are the signs on the new coefficients as expected? Are the new coefficients individually statistically significant? Write down and sketch the regression function for boys and girls separately. 2 Fall 2011 Rutgers University (c) The medical literature provides you with the following information for median height and weight of nine‐ to twelve‐year‐olds: Median Height and Weight for Children, Age 9‐12 Boysʹ Weight Boysʹ Height Girlsʹ Weight Girlsʹ Height 9‐year‐old 52 60 49 10‐year‐old 70 54 52 11‐year‐old 56 80 57 12‐year‐old 87 58.5 60 Due to sample of the experiment was skewed, some results are not completed. Therefore, you need to finish it by guessing the missing values. Insert two weight measures predictions using the estimation result in (b). (d) The F‐statistic for testing that the intercept and slope for boys and girls are identical is 2.92. Find the critical values at the 5% and 1% level, and make a decision. Allowing for a different intercept with an identical slope results in a t‐statistic for DFY of (–0.35). Having identical intercepts but different slopes gives a t‐statistic on (DFYHeight4) of (–0.35) also. Does this affect your previous conclusion? (Please state the hypotheses correctly to answer this question.) (e) Assume that you also wanted to test if the relationship changes by age. Briefly outline how you would specify the regression including the gender binary variable and an age binary variable (Older) that takes on a value of one for eleven to twelve year olds and is zero otherwise. Indicate in a table of two rows and two columns how the estimated relationship would vary between younger girls, older girls, younger boys, and older boys. (That is, four different equations are required to answer this question.) Instructor : H.H. Kim 3 Econometrics Answer: (a) For every inch above 4 feet, children of that age group gain roughly 4 pounds. A student who is 4 feet tall, weighs approximately 45.5 pounds. The regression explains 55 percent of the weight variation in children of that age group. (b) Shorter girls weight more than boys, and taller boys weigh more than girls on average. Given your prior expectations, this is somewhat unexpected. The coefficients involving the binary variable are statistically significant at conventional levels. The regressions for boys is = 36.27 + 5.32 × Height4. For girls it is = 53.60 + 3.49 × Height4. (c) The ʺXXʺ points mark a female, and the ʺXYʺ a male. The regression line predicts a 9‐year‐old boy to weigh 57.2 pounds, an 11‐year‐old boy to weigh 78.8 pounds, a 10‐year‐ old girl to weigh 67.6 and a 12‐year‐old girl to weigh 95.5 pounds. Hence the weights are quite close. 4 Fall 2011 Rutgers University (d) The critical value is 3.00 at the 5% level, and 4.61 at the 1% level. Hence you cannot reject equality of the two coefficients. The previous conclusion is unaffected since the test was for both hypotheses to hold simultaneously. The t‐statistics indicate that imposing the equality and testing for either the slope or the intercept to be significantly different between boys and girls, does not result in a different coefficient either. (e) Weight = β0 + β1DFY + β2Height4 + β3 (DFY × Height4) + β4Older + β5(Older × Height4) + u Boys Girls Younger Older 0 + 2 Height4 ( 0 + 4) + ( 2 + 5) Height4 ( 0 + 1) + ( 2 + 3) Height4 ( 0 + 1 + 4) + ( 2 + 3 + 5) Height4 ...
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This note was uploaded on 01/17/2012 for the course ECONOMICS 322 taught by Professor Derekdelia during the Fall '09 term at Rutgers.
- Fall '09