Week 8: Linear regression

Question 1

What kind of variables are needed for linear regression?

Answer 1

2 continuous

Question 2

What symbol is used for the correlation coefficient?

Answer 2

r

Question 3

What does r vary between?

Answer 3

-1 and +1

Question 4

What two pieces of information do you get from the correlation coefficient?

Answer 4

The direction (positive or negative)

The magnitude

Question 5

What happens in a positive relationship?

Answer 5

As one variable goes up, so does the other

Question 6

What happens in a negative relationship?

Answer 6

When one variable goes up, the other decreases

Question 7

The regression line helps to…

Answer 7

Predict other scores

Question 8

What is the regression equation?

Answer 8

= b (X) + a

Question 9

What is b in the regression equation?

Answer 9

The slope - how much change in the outcome for each increase in the predictor

Question 10

What do you multiply b with in the regression equation?

Answer 10

The value of the predictor variable

Question 11

What is a in the regression equation?

Answer 11

The intercept - value of the outcome variable when the predictor is 0

Question 12

How do you set up the data for a regression analysis in jamovi?

Answer 12

1x row per participant
1x column for each variable

all need to be continuous

Question 13

What is the independent variable called in linear regression?

Answer 13

Predictor variable

Question 14

What is the dependent variable called in linear regression?

Answer 14

Response or outcome variable

Question 15

How do you begin the analysis in jamovi?

Answer 15

Regression - linear regression

DV box: put the variable in that you want to predict the outcome of
Covariates: continuous predictors - put predictor in

Question 16

What fit measures and model coefficients do you ask for in a linear regression?

Answer 16

r
R squared
Adjusted r squared

ANOVA
Confidence intervals

Question 17

What does r give you?

Answer 17

The correlation between the IV and DV

Question 18

What does Rsquared tell you?

Answer 18

The proportion of the variance for a dependent variable that’s explained by an independent variable

Question 19

Adjusted R squared

Answer 19

like R squared but takes into account smaller sample sizes

Question 20

How do you generate a scatter plot in jamovi?

Answer 20

Exploration - scatter plot

Predictor in X axis box
Outcome into Y axis

Question 21

Which table gives you the values for the regression equation?

Answer 21

The Model coefficients box

Also gives you the ability to give t tests for the slope, and the intercept

Question 22

Which line definitely needs to be significant in the model coefficients box?

Answer 22

The slope - has to be different to zero

Both should be but especially the slope

Question 23

Regression becomes more reliable when….

Answer 23

The sample size increases

Question 24

Correlation and regression differences?

Answer 24

Correlation gives you the strength of the relationship between two continuous variables

Regression builds a model of this relationship to allow the prediction of other scores

Question 25

What does it mean if the slope is not different to 0?

Answer 25

The two variables are independent - knowing a score of one does not tell us anything about the other

Question 26

Correlation does not equal…….

Answer 26

causation

Question 27

What is extrapolation and how does it relate to regression?

Answer 27

the action of estimating or concluding something by assuming that existing trends will continue

You can only use the regression model to make predictions within the data range

Question 28

What kind of equation is used to describe curvy data?

Answer 28

Polynomial equations

Question 29

What are the different kinds of polynomials?

Answer 29

Quadratic
Cubic
Quartic and so on

Question 30

What is the equation for a quadratic equation?

Answer 30

Y = intercept + (slope1x(X)) + (slope2x(Xsquared)

Question 31

Each increase in the polynomial tests indicates..

Answer 31

A bend in the data line

Question 32

How do you do a quadratic regression in jamovi?

Answer 32

You need to first create another variable - IVsquared

• compute variable
• fx: IV*IV

Linear - Linear regression
DV - as normal
Covariates - normal IV and squared IV

In model builder tab - put normal IV into block one and the squared version into block 2

Question 33

Output of a quadratic regression in jamovi?

Answer 33

Model fit measures: tells you about the quadratic model in comparison to linear

Model coefficients: can use to make new t-tests as well as the quadratic equation

Model comparisons: tells you how much better the quadratic is - deltaF (df1, df2) = F, p = p (can see if the difference is worthwhile by looking at statistical significance)
Can see increases in Rsquared

Question 34

If a more complex model isnt improving the fit of the data but it looks better, what is it really doing?

Answer 34

Fitting the noise instead

Question 35

AIC and BIC?

Answer 35

How much information is lost by the model

Question 36

RMSEA?

Answer 36

Root mean square error of approximation
How much model misfit
<0.05 is a good fit

Question 37

What 3 coefficients do you have with a quadratic model?

Answer 37

Constant
Linear coefficient
Quadratic coefficient

Question 38

What do variables have to be able to do a trend analysis?

Answer 38

Quantitative, not qualitative

Question 39

How can we use a one-way ANOVA for trend analysis?

Answer 39

If we get a significant ANOVA, can ask for polynomial contrasts in the contrasts menu

The output here will be a list of possible models - the ones that are significant tell us more about the data

Question 40

What is trend analysis?

Answer 40

Helps to determine whether a linear or higher-order trend is required to describe the IV - DV relationship

Question 41

The most complex possible trend to describe a line that passes through every group mean is…

Answer 41

= (the number of levels of the IV) - 1

Question 42

What if the intercept = 0?

Answer 42

The slope is zero and the line is horizontal