Multiple Regression Flashcards
What is Linear Regression?
Linear Regression ask about the effect of one on another. It distinguishes between Independent variables (influencing) and the Dependent variable (being influenced).
Causality and Linear Regression
Line of best fit and ask about the relative variance explained by the straight line model relative to the unexplained variance (like a t-test)
Method of Least Squares
The straight line minimises the size of the squares resulting from drawing a vertical line from the point to the line and making this into a square
What is the equation for the Straight Line Model?
Y= mX + c
What is Y in the equation for the straight line?
Y is the predicted score on the DV
What is X in the equation for the straight line?
X is the score on the IV
What is m in the equation of the straight line?
m is the gradient or the slope (the steepness of the line)
What is c in the equation of the straight line?
c is the intercept (where the line crosses the y axis)
How do we calculate the straight line model with Y = mX + c
Multiple the score on the IV (X) by the gradient (m) and add the intercept (c)
Why is m important?
it tells us whether there is a positive, negative or neutral relationship between the DV and Ive, depending on the slope.
What would a positive m mean?
A line would have an upward slope
What would a neutral m mean?
A horizontal slope
What would a negative m mean?
A downward line/slope
How to calculate the best fit intercept
c = Y(mean) - m X(mean)
What is the SST?
Total variability in data - difference between each Y value and mean value of Y
What is the SSR?
Difference between observed Ys and those predicted by the model: Residual/ unexplained variance
SSM is calculated by what equation?
SSm = SST - SSR
What is the difference between the Set and the SSR?
The measure of how much variance is explained.
How do you calculate the total variance?
SST = the sum of (Y- Ymean) and then squared
How to calculate the SS residuals?
Differences between the Y value and the participant’s predicted Y value.
SSR = Sum of (Y -Ypred) squared
How to calculate the SSM
SSm = SST - SSR
What does Rsquared tell us?
The proportion of the variance in the DV is explained by the IV
What is the equation for Rsquared?
Rsquared = SSM/ SST
How to get the mean of X?
Add up all the scores of the independent variable and average
How to get the mean of Y?
Add up all the scores of the dependent variable and average
How to calculate the gradient (m)?
The sum of (X-Xmean) x (Y-Ymean)
___________________________
sum of (X-Xmean) squared
How do you calculate the intercept c?
C = Ymean - m(Xmean)
