8. Calculating SSR, SSE, SST, and R-squared Suppose you are interested in studying the effects of education on wages. You gather four data points and use ordinary least squares (OLS) to estimate the following simple linear model: wage = Bo + Bieduc + u where wage - hourly wage in dollars educ - years of formal education After running your regression, you decide to examine how the fitted values of wages from your regression compare to the actual wages in your data set. These data are summarized in the following table: residuals obsno twage, wage, u = wage, - twage 1 15 14.7 0.3 2 19 19.9 -0.9 3 26 25.1 0.9 4 30 30.3 -0.3 Based on the data in the table, the explained sum of squares (SSE) is Based on the data in the table, the residual sum of squares (SSR) is Based on the data in the table, the total sum of squares (SST) is While you are skeptical of your OLS regression due to the low number of data points, you decide to calculate the R-squared of the regression to understand how well the independent variable educ explains the dependent variable wage. The resulting Re is
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.
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