Linear reggression Flashcards
What is linear regression
To predict one variable from another
= inferential statistics
Regression coefficient
b = the slope of the line
Residual term, ε
the difference between the score predicted by the line for participant i and the score that participant i actually obtained.
Intercept
b0 = where the line crosses the Y-axis
Residuals
The deviations from the data point to the regression line
Goodness of fit
How well does the model fit the data
Total sum of squares (SSt)
Sum of squared differences between the dependent variable and the MEAN
Residual sum of squares (SSr)
Sum of squares calculated on the regression line
Model sum of squares (SSm)
The difference between the residual model than the mean model
Large SSm = large difference, the regression is a lot better than the mean
R2
R2 represents the amount of variance in the outcome explained by the model (SSM) relative to how much variation there was to explain in the first place (SST).
R2 = SSm / SSt
- As percentage it represents the per- centage of the variation in the outcome that can be explained by the model
F-ratio
A measure of how much the model has improved the prediction of the outcome com- pared to the level of inaccuracy of the model.
F = MSm / MSr
Mean squared for the model divided by the mean squared of residuals
Large F-ratio = Good model
If a model is good, then we expect the improvement in prediction due to the model to be large (so MSM will be large) and the difference between the model and the observed data to be small (so MSR will be small).
F’s similarities with t-test?
Like F, the t-statistic is also based on the ratio of explained variance against unex- plained variance or error.
