Chapter 10: Simple Linear Regression Flashcards
Regression analysis
Allows us to test hypotheses about the relationship between two variables, by quantifying the strength of the relationship between the two variables, and to use one variable to make predictions about the other variable.
Sum of squares total (SST)
A measure of the total variation in the dependent variable in a simple linear regression. It is calculated by subtracting the mean of the observed values Y¯ from each of the observed values Yi, squaring each of these differences, and then summing all of these squared differences.
Simple linear regression (SLR)
An approach for estimating the linear relationship between a dependent variable and a single independent variable by minimizing the sum of the squared deviations between the fitted line and the observed values.
Regression coefficients
The collective term for the intercept and slope coefficients in the regression model.
Residual
The amount of deviation of an observed value of the dependent variable from its estimated value based on the fitted regression line.
Sum of squares error (SSE)
A measure of the total deviation between observed and estimated values of the dependent variable. It is calculated by subtracting each estimated value Y^i from its corresponding observed value Yi, squaring each of these differences, and then summing all of these squared differences.
Homoskedasticity
Constant variance across all observations.
Heteroskedasticity
Non-constant variance across all observations.
Estimated parameters
The intercept and slope of the fitted line.
Sum of squares regression (SSR)
A measure of the explained variation in the dependent variable, calculated as the sum of the squared differences between the predicted value of the dependent variable, Y ̂_i, based on the estimated regression line, and the mean of the dependent variable, Ȳ.
Coefficient of determination (R2)
The percentage of the variation of the dependent variable that is explained by the independent variable. It is a measure of goodness of fit of a regression model.
Mean square regression (MSR)
Calculated as the sum of squares regression (SSR) divided by the number of independent variables in the regression model. In simple linear regression, there is only one independent variable, so MSR equals SSR.
Mean square error (MSE)
Calculated as the sum of squares error (SSE) divided by the degrees of freedom, which are the number of observations minus the number of independent variables minus one. Since simple linear regression has just one independent variable, the degrees of freedom calculation is the number of observations minus 2.
Standard error of the slope coefficient
Calculated for simple linear regression by dividing the standard error of the estimate by the square root of the variation of the independent variable.
Indicator variable
A variable that takes on only one of two values, 0 or 1, based on a condition. In simple linear regression, the slope is the difference in the dependent variable for the two conditions. Also referred to as a dummy variable.
