Simple Linear Regression Flashcards
What is the dependent variable (DV)?
It is the Y variable and it’s the variable we are trying to explain.
What is a simple linear regression?
It only has one independent variable and that there is a linear relationship between the DV and IV
What is the independent variable (IV)?
It is the X variable and it’s the explanatory variable.
What is b0?
It’s the intercept (if X is zero, then Y will be the intercept, i.e. where the regression line crosses the Y axis).
Blank is regressed on blank?
Y is regressed on X.
What is the error term?
It is the residual or the portion of the DV that cannot be explained by the IV.
What does the regression line do in terms of the residuals?
compute a line of best fit that minimizes the sum of the squared deviations between the observed values of Y and the predicted values (the regression line)
Does the sign (neg or pos) on the coefficent indicate the neg or pos correlation?
Yes, the sign on the coefficient is determined by the covariance.
What are the four assumptions of simple linear regressions?
1) Linearity: the relationship between X and Y is linear in the parameters b naught and b 1 (neither is multiplied or divided by another regression parameter
2) Homoskedasticity: The variance of the error term is the same for all observations (a violation indicates the data series may come from 2 different populations (corss sectional) or regimes (time series)
Does the sign (neg or pos) on the coefficient indicate the neg or pos correlation?
Yes, the sign on the coefficient is determined by the covariance.
What are the four assumptions of simple linear regressions?
1) Linearity: the relationship between X and Y is linear in the parameters b naught and b 1 (neither is multiplied or divided by another regression parameter
2) Homoskedasticity: The variance of the error term is the same for all observations (a violation indicates the data series may come from 2 different populations (cross-sectional) or regimes (time series)
3) Independence: the pairs (X and Y) are independent of each other and the error term is uncorrelated across observations (no serial correlation)
4)
What are the four assumptions of simple linear regressions?
1) Linearity: the relationship between X and Y is linear in the parameters b naught and b 1 (neither is multiplied or divided by another regression parameter
2) Homoskedasticity: The variance of the error term is the same for all observations (a violation indicates the data series may come from 2 different populations (cross-sectional) or regimes (time series)
3) Independence: the pairs (X and Y) are independent of each other and the error term is uncorrelated across observations (no serial correlation)
4) Normality: The error term is normally distributed and does not depend on the value of X
What is the coefficient of determination?
it’s R^2 (R-squared), measures the goodness of fit, and measures the fraction of the total variation in the dependent variable that is explained by the independent variable.
What is the formula for the Total sum of squares?
What is the formula for the sum of squared errors (SSE)?
unexplained
What is the formula for regression sum of squares (SSR)?
explained
What is the equation for R^2 (R-squared)
SSR/SST = Regression sum of squares/Total sum of squares = explained variance/total variance
What’s the relationship between the total sum of squares (SST), sum of squared errors (SSE), and regression sum of squares (SSR)?
total SS = unexplained SS + explained SS
Does R squared offer a measure of statistical significance?
No, but the F test does
For the F test, what are the hypothesis tests for one independent variable and more than one independent variable?
What is the formula for the F-test?
What does the ANOVA table look like?
What is the formula for the standard error of the estimate and what is it doing?
