Correlation & Regression

Question 1

How do we get the proportion of explained variance from two continuous variables?

Answer 1

Correlate the two variables and square it

Question 2

Why can’t we just use covariance?

Answer 2

Not standardised

Question 3

what do you have to do to a correlation first in order to test for significance?

Answer 3

Convert to a t score

Question 4

What does 1 - r^2 represent?

Answer 4

unexplained variance

Question 5

What does a partial correlation do?

Answer 5

Examines the correlations between variables x, y and a confound z in order to remove or control for the variable z

Question 6

What differences are there between a partial correlation and a covariance analysis

Answer 6

In C.A the independent variables are categorical.

ANCOVA is also a linear model while P.C is using correlations

Question 7

What do the B’s stand for in model’s?

Answer 7

Parameter estimates

Question 8

What assumptions does regression operate under?

Answer 8

Sensitivity (to outliers)

Homoscedasticity ( variance of residuals should be equal across all expected values)

Question 9

What can be used in order to control for outliers? (3)

Answer 9

Cook’s distance (<1)
Mahalonobis (<11 at N= 30)
Laverage ( The average leverage value is defined as (k + 1/n)

Question 10

How do you test for homoscedacticity?

Answer 10

Look at scatterplot of standardised: expected values x residuals. Roughly round shape is needed

Question 11

In the equation for regression, what does b1 represent?

Answer 11

The regression slope

Question 12

In the equation for regression, what does b0 represent?

Answer 12

The intercept of the regression slope and the y axis

Question 13

What t test is used for regression?

Answer 13

One sample t test of b1

Question 14

What is meant by the covariance?

Answer 14

the averaged sum of combined deviations.

Question 15

What formulas can be used in r for correlations and covariances?

Answer 15

• cor(x, y, “everything”, “pearson”)

* cov(x, y, “everything”, “pearson”)

Question 16

How do you calculate a correlation in spss?

Answer 16

Go to analyze > correlate > bivariate. Enter the variables in variables. You can choose which correlation coefficients you want: Pearson, Kendall’s tau-b, or Spearman.

Question 17

How do you calculate a partial correlation in spss?

Answer 17

Go to analyzeàcorrelateàpartial. Place the variables under variables and the variable you want to control for under controlling for. Click on optionsàzero-order correlations to get the r that you would get if you didn’t control for the third variable.

Question 18

What is meant by simple linear regression?

Answer 18

regression with one continuous independent variable and one continuous dependent variable. It is used to see if you can predict the values of the dependent variable using the independent variable.

Question 19

What might the hypotheses for a simple linear regression look like?

Answer 19

• H0:X can’t predict Y; b1 =0; t=0; orF=0

* Ha: X can predict Y; b1 0; t 0; orF>0

Question 20

How are the degrees of freedom calculated in linear regression?

Answer 20

df = n - p - 1

• n = the number of entities
• p = the number of predictors

Question 21

How do we calculate the fit of the model?

Answer 21

To test the fit of the model we can perform an F-test.

n-p-1)r^2 / p(1-r^2

Question 22

What would an R^2 of 37.4 in the spss output mean?

Answer 22

x can account for 37.4% of the variance in y

Question 23

How do you calculate a linear regression in spss?

Answer 23

Go to analyze > regression > linear. Place the dependent variable in dependent and the independent variable in independent(s).
Under statistics we select model fit, R squared change, descriptives, part and partial correlations and collinearity. Under save we tick mahalanobis, Cook’s and leverage values to get an idea of extreme outliers in the data. It’s also good to tick unstandardised under predicted values, to see what the expected value in the data set is.