ex2_2011ak (1)

# Ex2_2011ak(1) - Sociology 63993 Exam 2 Answ er Key April 1 2011 I True-False(20 points Indicate whether the following statements are true or false

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Sociology 63993—Exam 2—Page 1 S o c i o l o g y 63993 E x a m 2 A n s w e r K e y A p r i l 1 , 2 0 1 1 I. True-False. (20 points) Indicate whether the following statements are true or false. If false, briefly explain why. 1. A researcher computes a variable X 4 = X 2 + X 3 . She then estimates the following two models using OLS regression: Y = 1 X 1 + 2 X 2 + 3 X 3 + Y = 1 X 1 + 4 X 4 + She can use an incremental F test to determine which of these two models is better. True. Since X 4 = X 2 + X 3 , the incremental F is a test of whether or not 2 = 3 . 2. A researcher runs the following: . webuse nhanes2f, clear . gen femage = female * age . reg health female age femage Source | SS df MS Number of obs = 10335 -------------+------------------------------ F( 3, 10331) = 549.60 Model | 2069.28161 3 689.760537 Prob > F = 0.0000 Residual | 12965.7398 10331 1.2550324 R-squared = 0.1376 -------------+------------------------------ Adj R-squared = 0.1374 Total | 15035.0214 10334 1.4549082 Root MSE = 1.1203 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- female | -.2752255 .0648373 -4.24 0.000 -.4023191 -.1481319 age | -.0280887 .0009315 -30.15 0.000 -.0299146 -.0262627 femage | .0043295 .0012822 3.38 0.001 .0018162 .0068428 _cons | 4.78594 .0469616 101.91 0.000 4.693886 4.877994 ------------------------------------------------------------------------------ These results show that age has a negative effect on the health of males and a positive effect on the health of females. False. The effect of age is less negative for females (-.0280887 + .0043295 = -.0237592) but it is still negative. 3. A researcher has included several extraneous variables in her model. The larger her sample, the more serious this problem will be. False. Adding extraneous variables increases standard errors. Larger sample sizes decrease standard errors. 4. A researcher regresses income on education. She does not include any dummy variables or interaction terms involving gender. One implication of this model is that, if it is true, the mean income for men will be the same as the mean income for women. False. If men and women differ in their mean levels of education, they will also differ in their mean incomes.

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Sociology 63993—Exam 2—Page 2 5. A researcher is interested in the relationship between bmi (Body Mass Index) and health. She does the following: . webuse nhanes2f, clear . gen bmi = weight/ (height/100)^2 . gen bmi2 = bmi * bmi . reg health bmi bmi2 Source | SS df MS Number of obs = 10335 -------------+------------------------------ F( 2, 10332) = 111.24 Model | 316.928298 2 158.464149 Prob > F = 0.0000 Residual | 14718.0931 10332 1.4245154 R-squared = 0.0211 -------------+------------------------------ Adj R-squared = 0.0209 Total | 15035.0214 10334 1.4549082 Root MSE = 1.1935 ------------------------------------------------------------------------------ health | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- bmi | .0072049 .0152456 0.47 0.637 -.0226794 .0370892 bmi2 | -.0007416 .0002646 -2.80 0.005 -.0012601 -.000223 _cons | 3.731409 .2147848 17.37 0.000 3.31039 4.152429 ------------------------------------------------------------------------------ Based on these results, she should conclude that bmi is not related to health. False. The results indicate that there is a curvilinear relationship between bmi and health. Increases in body mass index are good up to point, but after that further increases are harmful. (In other words, it isn’t good to be obese.) II. Path Analysis/Model specification (25 pts). A sociologist believes that the following model describes the relationship between X1, X2, X3, and X4. All her variables are in standardized form. The estimated value of each path in her model is included in the diagram. a. (5 pts) Write out the structural equation for each endogenous variable, using both the names for the paths (e.g. β 42 ) and the estimated value of the path coefficient.
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## This note was uploaded on 02/29/2012 for the course SOC 63993 taught by Professor Richardwilliams during the Spring '11 term at Notre Dame.

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Ex2_2011ak(1) - Sociology 63993 Exam 2 Answ er Key April 1 2011 I True-False(20 points Indicate whether the following statements are true or false

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