a) Is the relationship between Age and Earn statistically significant? b) The variance of the error term and the variance of the dependent variable are related. Given the distribution of earnings, do you think it is plausible that the distribution of errors is normal? c) Construct a 95% confidence interval for both the slope and the intercept.
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.
You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, yielded the following result:
Earn = 239.16 + 5.20×Age R2 = 0.05, SER = 287.21
SE: (20.24) (0.57)
where Earn and Age are measured in dollars and years respectively.
a) Is the relationship between Age and Earn statistically significant?
b) The variance of the error term and the variance of the dependent variable are related. Given the distribution of earnings, do you think it is plausible that the distribution of errors is normal?
c) Construct a 95% confidence interval for both the slope and the intercept.
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