Regression Module

Question 1

Explain simple linear regression

Answer 1

used to examine if the DV can be predicted by the IV
e.g., can the results (DV) be predicted by the arrival time (IV)?

Question 2

What are the three differences between simple linear regression and correlation

Answer 2

> asymmetry vs symmetry relationship
2 variables with relationship vs 2 variables without relationships
look for predictions vs look for correlations

Question 3

What is the formula of simple regression model equation, full simple regression equation, and the residual

Answer 3

Y(hat) (predicted DV, which is the Y axis) = a + bX(i) (observed IV, which is the X axis)

Y(i) (observed DV, y axis) = a + bX(i) + e (residual)

residual = observed - predicted of the DV (y axis)

Question 4

what does the best fitting line mean, what is the method that is used to obtain the line, and what are the residuals called

Answer 4

the least residual, the line that is drawn closes to all points on the model

the method of least square
sum of all squared residuals

residuals above the line = positive residuals
residuals below the line = negative residuals

Question 5

What are the two things that are assessed after completing the regression model?

Answer 5

the strength of the model (Rˆ2) and whether the model can be used for the population (rhoˆ2)

Question 6

explain Rˆ2

Answer 6

> measures the variation predicted of the DV
ranges between 0-1
0 = no prediction of the DV; 1 = perfect prediction of the DV
Rˆ2 x 100% = the percentage of variation that the model can predict

Question 7

explain rhoˆ2

Answer 7

run a f-test and NHST
H0 = rhoˆ2 = 0 (i.e., IV does not significantly predict the DV)
H1 vice versa

run f-test
df(1) = number of IV = k
df(2) = n - k - 1

if the F-score > critical + p < critical
can reject null hypothesis and accept H1

Question 8

What is the regression coefficient, and what does it determine

Answer 8

b
the sign of b determines the direction of the model

the size of b determines the degree of the model

Question 9

What will happen when:
1. b = +

2. b = -

Answer 9

> the model is positive
if IV increases by one unit, DV also increases by b unit
if IV decreases by one unit, DV also decreases by b unit

> the model is negative
if IV increases by one unit, DV decreases by b unit
if IV decreases by one unit, DV increases by b unit

c x b: c = number of units increases

Question 10

explain the difference between unstandardised and standardised regression model

Answer 10

unstandardised
> used to predict by how many DV units are changed due to the unit change of IV
> usually used when the variables are interpretable

standardised
> used to predict by how many DV SD is changed when the SD of the IV is changed
> useful when the variables are uninterpretable (attitude)