Week 2 Multiple regression

Question 1

What does a regression analysis do?

Answer 1

A regression analysis is a reliable method of identifying which variables have an impact on a topic of interest. It is about predicting a single quantitative DV from multiple quantitative and/or qualitative variables.

Question 2

What does a linear regression predict?

Answer 2

a single outcome variable: a quantitative outcome variable, usually a quasi-continuous one. Linear regression is focused on predicting an outcome (DV) using predictor variables (IVs).

Question 3

What are some other types of regression?

Answer 3

Logistic regression (used for dichotomous or polytomous outcomes)

Non-linear regression
Special nonlinear functions AND
Multiple predictors and multiple SEM or PLS (partial least squares regression.

Question 4

What is linear regression based on?

Answer 4

Pearson correlation and least squares.

Question 5

How can you linearise a nonlinear item?

Answer 5

Log transform

Question 6

In regression we predict…

Answer 6

Y from X (Y1 = A +BX)
Y is the predicted outcome
X is the predictor variables
A is the intercept or constant
B is regression coefficients (slopes): how much each X contributes to Y.-

Question 7

What is variance?

Answer 7

The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean and thus from every other number in the set.

Question 8

What is R2 = (SSreg/SSy)

Answer 8

Total variance explained

Question 9

What is Y1 – Y

Answer 9

Error

Question 10

What is ∑(Y – Y1)2

Answer 10

Least squares solution

Question 11

What are the four basic regression steps?

Answer 11

Step 1 Prepare data

Step 2 Run regression software (enter DV and IVs, choose options)

Step 3 Interpret parameter estimates (intercept and regression coefficients, R2, ANOVA)

Step 4 Check diagnostics (Check for linearity, normality, homoscedasticity, independence of errors, outliers, multicollinearity and singularity, measurement error).

Question 12

What are multiple regression coefficients telling us?

Answer 12

In regression with multiple independent variables, the coefficient tells you how much the dependent variable is expected to increase when that independent variable increases by one, holding all the other independent variables constant.

Question 13

What is a correlation test in SPSS?

Answer 13

A (Pearson) correlation is a number between -1 and +1 that indicates to what extent 2 quantitative variables are linearly related. It’s best understood by looking at some scatterplots.

Question 14

What is the Variables Entered/Removed output in regression?

Answer 14

A summary of predictors added and in how many blocks. Also the method of entry (enter versus stepwise)

Question 15

What is the model summary output in regression?

Answer 15

This table provides the R and R2 values. The R value represents the simple correlation and indicates the degree of correlation.
The R2 value (the “R Square” column) indicates how much of the total variation in the DV can be explained by the IV.

Question 16

What is the ANOVA output telling us in regression?

Answer 16

It is the sum of the square of the difference between the predicted value and mean of the value of all the data points.
Example: From the ANOVA table, the regression SS is 6.5 and the total SS is 9.9, which means the regression model explains about 6.5/9.9 (around 65%) of all the variability in the dataset.

Question 17

What does the coefficients output table tell us?

Answer 17

The Coefficients table provides us with the necessary information to predict the DV from IV, as well as determine whether the IV contributes statistically significantly to the model (by looking at the “Sig.” column). Furthermore, we can use the values in the “B” column under the “Unstandardized Coefficients” column, as shown below:
B = 0.176 – For every one unit increase in social identity score (IV) there is a 0.176 increase in anxiety score (DV).
β – For every one standard deviation unit increase in social identity there is a .204 standard deviation unit increase in anxiety score. This represents a small to medium effect (Cohen’s rule of thumb = .1 small, .3 medium, .5 large)

Question 18

In the coefficient output table, what do the unstandardised coefficient regression and confidence intervals tell us?

Answer 18

B = 0.152 – For every one unit increase in rating of CBT program efficacy there is a 0.152 (from unstandardised coefficient) increase in anxiety score.

Confidence interval -We are 95% confident that the actual increase in anxiety score would fall between 0.074 and 0.229 (from confidence interval)

Question 19

What is a zero-order correlation?

Answer 19

simply refers to the correlation between two variables (i.e., the independent and dependent variable) without controlling for the influence of any other variables.

Question 20

What is partial correlation?

Answer 20

Derived from the ‘part’ column of the output. Need to square the number and that percentage is the amount that uniquely explains that part of variation in the DV.

Question 21

What is ‘tolerance’ in the collinearity statistics column of the coefficients output?

Answer 21

The amount of variance unexplained by the predictors.

Question 22

How do we check for multivariate outliers?

Answer 22

Residual statistics output – Mahalanobis Distance gives us a measure of how far each participants score is from the multivariate group centroid (globe (distance from centre).
Compare maximum Mahal to .001 of chi square table.

Question 23

How do you check for assumption of normality of residuals?

Answer 23

Histogram – does it look bell curvy?

P-P plot – do data points conform to the diagonal line?

Question 24

How do you do visual checks of assumptions of homoskedasticity and linearity of residuals?

Answer 24

Scatterplot!!
Homoskedasticity – any signs of unevenness or fanning?
Linearity – Any sign of curvature?