Suppose we are interested in the effect of gender on incomeand we estimate a model in which income is the dependentvariable and the regressor is a dummy variable that takes thevalue 1 if the person is a man and O if the person is a woman.If we instead estimate a model that includes a dummy variablefor women (takes value 1 if woman and 0 if man), thenThe fit of the model will change.We will get a different conclusion for testing a null hypothesis thatthere is no gender effect.The coefficient on the dummy variables will differ across models,but the estimated difference of mean income between men andwomen will not change.The coefficient on the dummy variables will be exactly the same.

It is required to identify the correct statement regarding a dummy variable in regression analysis.

Suppose we are interested in the effect of gender on income and we estimate a model in which income is the dependent variable and the regressor is a dummy variable that takes the value 1 if the person is a man and O if the person is a woman. If we instead estimate a model that includes a dummy variable for women (takes value 1 if woman and O if man), then The fit of the model will change. We will get a different conclusion for testing a null hypothesis that there is no gender effect. The coefficient on the dummy variables will differ across models, but the estimated difference of mean income between men and women will not change. The coefficient on the dummy variables will be exactly the same.

Suppose we are interested in the effect of gender on income and we estimate a model in which income is the dependent variable and the regressor is a dummy variable that takes the value 1 if the person is a man and O if the person is a woman. If we instead estimate a model that includes a dummy variable for women (takes value 1 if woman and O if man), then The fit of the model will change. We will get a different conclusion for testing a null hypothesis that there is no gender effect. The coefficient on the dummy variables will differ across models, but the estimated difference of mean income between men and women will not change. The coefficient on the dummy variables will be exactly the same.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Suppose that a researcher, using wage data on 200 randomly selected male workers and 240female workers, estimates the OLS regressionW age ˆ =10(0.2)+2(0.4)× M ale, R2 = 0.10, SER = 4,where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if theperson is a male and 0 if the person is a female. Define the wage gender gap as the difference inmean earnings between men and women.1. What is the estimated gender gap?2. Is the estimated gender gap significantly different from 0? (Compute the p-value for testingthe null hypothesis that there is no gender gap.)13. Construct a 95% confidence interval for the gender gap.4. In the sample, what is the mean wage of women? Of men?5. Another researcher uses these same data but regresses Wages on Female, a variable that isequal to 1 if the person is female and 0 if the person a male. What are the regression estimatescalculated from this regression?W age ˆ = _ + _ × F emale, R2 = _, SER = _.
Suppose that a least squares regression line equation is ˆy = 1.65 − 2.20x and the actual y value corresponding to x = 10 is −19, what is the residual value corresponding to y = −19?
The t-test on individual model coefficients is a test on the significance of the coefficient of apredictor as if it were the last variable added to a model that already contains all the otherpredictors. (true or false?)
An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) test
Suppose a least-squares regression line is given by y=4.302x−3.293. What is the mean value of the response variable if x=20? μy20=_______? (Round to one decimal place as needed.)
Here, mean of X is 3 and the mean of Y is 7. The regression line that predicts Y from X necessarily goes through the point (3,7). True False
8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
A regression line describes the relationship between the dependent and independent variables and can be used to estimate specific points for x or y, provided an individual is supplied with the values of all the other variables but one. True or false
Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is NOT true in the multiple linear regression outputs? In the F-test ANOVA result, if Ho is rejected, this means that the regression model overall predicts the dependent variable significantly well. If a predictor is having a significant impact on our ability to predict the outcome then the regression coefficient b should be significantly different from 1.0. The F-test ANOVA assesses all of the regression coefficients jointly whereas the t-test for each coefficient examines them individually. It is possible that a model is significant, but not enough to conclude that any individual variable is significant.
Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25. In a sample of n=50 people who recently received speeding tickets, 33 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha=0.5. A. what is the proposed analysis and why you chose this? B. Test assumptions and make a decision with evidence? C. Inferential statics and P values? D. Final decision and Conclusion?
Suppose that you plot the residuals from a regression of GDP on the unemployment rate and you get Figure 1. You would conclude that the error terms are Select one: a. definitely autocorrelated. b. possibly autocorrelated and you would perform a correction for heteroskedasticity. c. possibly autocorrelated and you would perform a formal test for autocorrelation. d. likely not autocorrelated.