Multiple Regression

Question 1

What is Linear Regression?

Answer 1

Linear Regression ask about the effect of one on another. It distinguishes between Independent variables (influencing) and the Dependent variable (being influenced).

Question 2

Causality and Linear Regression

Answer 2

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)

Question 3

Method of Least Squares

Answer 3

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

Question 4

What is the equation for the Straight Line Model?

Answer 4

Y= mX + c

Question 5

What is Y in the equation for the straight line?

Answer 5

Y is the predicted score on the DV

Question 6

What is X in the equation for the straight line?

Answer 6

X is the score on the IV

Question 7

What is m in the equation of the straight line?

Answer 7

m is the gradient or the slope (the steepness of the line)

Question 8

What is c in the equation of the straight line?

Answer 8

c is the intercept (where the line crosses the y axis)

Question 9

How do we calculate the straight line model with Y = mX + c

Answer 9

Multiple the score on the IV (X) by the gradient (m) and add the intercept (c)

Question 10

Why is m important?

Answer 10

it tells us whether there is a positive, negative or neutral relationship between the DV and Ive, depending on the slope.

Question 11

What would a positive m mean?

Answer 11

A line would have an upward slope

Question 12

What would a neutral m mean?

Answer 12

A horizontal slope

Question 13

What would a negative m mean?

Answer 13

A downward line/slope

Question 14

How to calculate the best fit intercept

Answer 14

c = Y(mean) - m X(mean)

Question 15

What is the SST?

Answer 15

Total variability in data - difference between each Y value and mean value of Y

Question 16

What is the SSR?

Answer 16

Difference between observed Ys and those predicted by the model: Residual/ unexplained variance

Question 17

SSM is calculated by what equation?

Answer 17

SSm = SST - SSR

Question 18

What is the difference between the Set and the SSR?

Answer 18

The measure of how much variance is explained.

Question 19

How do you calculate the total variance?

Answer 19

SST = the sum of (Y- Ymean) and then squared

Question 20

How to calculate the SS residuals?

Answer 20

Differences between the Y value and the participant’s predicted Y value.

SSR = Sum of (Y -Ypred) squared

Question 21

How to calculate the SSM

Answer 21

SSm = SST - SSR

Question 22

What does Rsquared tell us?

Answer 22

The proportion of the variance in the DV is explained by the IV

Question 23

What is the equation for Rsquared?

Answer 23

Rsquared = SSM/ SST

Question 24

How to get the mean of X?

Answer 24

Add up all the scores of the independent variable and average

Question 25

How to get the mean of Y?

Answer 25

Add up all the scores of the dependent variable and average

Question 26

How to calculate the gradient (m)?

Answer 26

The sum of (X-Xmean) x (Y-Ymean)
___________________________
sum of (X-Xmean) squared

Question 27

How do you calculate the intercept c?

Answer 27

C = Ymean - m(Xmean)