a) You estimate the following polynomial regression model wage over Age, A g e 2, together with a dummy variable Female that takes on the value of one for females and is zero otherwise: Model 1: w a g e = 10. 04 + 2.10 A g e + 0.05 A g e 2 + 13.19 F e m a l e , ( 0.45 ) ( 0.20 ) ( 0.003 ) ( 2.45 ) Use a t-test for the significance of the coefficient of A g e 2. Please write down its corresponding test hypotheses H 0, H 1 and your conclusion, i.e., if reject the null hypothesis or not. (b) Predict the wage for a Male 30-years-old worker. And predict the wage for a Male 40-years-old worker. Furthermore, for a Male worker, if Age increase from 30 to 40, how does wage expect to change? (c) Please use a sentence to interpret the coefficient of variable Female. (d) You run another regression as below. Model 2: w a g e = 11.44 + 1.70 A g e + 0.01 A g e 2 + 13.16 F e m a l e ( 0.58 ) ( 0.30 ) ( 0.004 ) ( 2.65 ) − 0.002 F e m a l e × A g e + 0.005 F e m a l e × A g e 2 , ( 0.045 ) ( 0.007 ) To test H 0 : β 4 = β 5 = 0 in Model 2, i.e., the coefficients of the last two interaction terms are jointly zero, the computer returns the F-statistic of 1.23 with p-value of 0.04. Given these test results, please write down your conclusion, i.e., if reject the null hypothesis H 0 or not. (e) Based on the F-test result in part (f), which regression between the two shall we choose, model 1 or model 2. Why?
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.
a) You estimate the following polynomial regression model wage over Age, A g e 2, together with a dummy variable Female that takes on the value of one for females and is zero otherwise:
Model 1:
w a g e = 10. 04 + 2.10 A g e + 0.05 A g e 2 + 13.19 F e m a l e ,
( 0.45 ) ( 0.20 ) ( 0.003 ) ( 2.45 )
Use a t-test for the significance of the coefficient of A g e 2. Please write down its corresponding test hypotheses H 0, H 1 and your conclusion, i.e., if reject the null hypothesis or not.
(b) Predict the wage for a Male 30-years-old worker. And predict the wage for a Male 40-years-old worker. Furthermore, for a Male worker, if Age increase from 30 to 40, how does wage expect to change?
(c) Please use a sentence to interpret the coefficient of variable Female.
(d) You run another regression as below.
Model 2:
w a g e = 11.44 + 1.70 A g e + 0.01 A g e 2 + 13.16 F e m a l e
( 0.58 ) ( 0.30 ) ( 0.004 ) ( 2.65 )
− 0.002 F e m a l e × A g e + 0.005 F e m a l e × A g e 2 ,
( 0.045 ) ( 0.007 )
To test H 0 : β 4 = β 5 = 0 in Model 2, i.e., the coefficients of the last two interaction terms are jointly zero, the computer returns the F-statistic of 1.23 with p-value of 0.04. Given these test results, please write down your conclusion, i.e., if reject the null hypothesis H 0 or not.
(e) Based on the F-test result in part (f), which regression between the two shall we choose, model 1 or model 2. Why?
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