Suppose that a researcher, using wage data on 200 randomly selected male workers and 240 female workers, estimates the OLS regression W 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 the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean 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 testing the null hypothesis that there is no gender gap.) 1 3. 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 is equal to 1 if the person is female and 0 if the person a male. What are the regression estimates calculated from this regression? W age ˆ = _ + _ × F emale, R2 = _, SER = _.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Suppose that a researcher, using wage data on 200 randomly selected male workers and 240
female workers, estimates the OLS regression
W 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 the
person is a male and 0 if the person is a female. Define the wage gender gap as the difference in
mean 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 testing
the null hypothesis that there is no gender gap.)
1
3. 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 is
equal to 1 if the person is female and 0 if the person a male. What are the regression estimates
calculated from this regression?
W age ˆ = _ + _ × F emale, R2 = _, SER = _.
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