Correlation & Multiple Regression

Question 1

What is correlation?

Answer 1

An association or dependency between two independently observed variables.

Question 2

What type of graph is used for correlations?

Answer 2

scatterplots

Question 3

A Pearson correlation coefficient of -1.0 means X and Y are____

Answer 3

exactly inverse to one another

Question 4

Which measure of association should be used when both variables are interval/ratio e.g temperature ?

Answer 4

Pearson’s coefficient

Question 5

Which measure of association should be used when both variables are ordinal (rank) ?

Answer 5

Spearman’s/ Kendall’s rank coefficient

Question 6

Which measure of association should be used when both variables are true dichotomous e.g male/female or yes/no ?

Answer 6

Phi coefficient

Question 7

Point-biserial coefficient is used when one variable is ____ and the other variable is _____

Answer 7

true dichotomy and interval

Question 8

If there are more than 2 variables and you want to assess the relationship of one pair after accounting for another pair. What type of correlation is this?

Answer 8

partial correlation

Question 9

What is multiple linear regression?

Answer 9

Similar concept to correlation.

It describes the relationship between one or more predictor variables and a single criterion variable.

Question 10

The goal of a regression model is finding the best fit between the model and the observation. This is done by adjusting the value of the _____________ until the prediction error is minimised.

Answer 10

regression coefficient

Question 11

What is the residual sum of squares?

Answer 11

A statistical technique used to measure the amount of variance in a data set that is not explained by a regression model.

Question 12

You can assess the goodness of fit of a regression model by using a multiple correlation coefficient (R). What is this a correlation between?

Answer 12

A correlation between the predicted values and the observed values

Question 13

You can assess the goodness of fit of a regression model by using a coefficient of determination (R^2). This is simply the proportion of ______ explained by the ______.

Answer 13

The proportion of variance measured by the regression model.

Question 14

F-ratios in ANOVA can be used to assess the goodness of fit of the linear regression model. What does a high F-ratio indicate?

Answer 14

a good model, decreased prediction error

Question 15

A simultaneous (standard) multiple regression approach is used when ____

Answer 15

no a priori model is assumed and all predictor variables are fit together

Question 16

A stepwise approach is not a good approach because_____

Answer 16

it will always overfit the data

Question 17

If a relationship is already known but we want to account for it. What multiple regression approach is taken?

Answer 17

hierarchical

Question 18

Cook’s distance measures the extremity of an _____; values greater than 1 are cause for concern.

Answer 18

outlier

Question 19

Define scedasticity.

Answer 19

scedasticity refers to the distribution of the residual error relative to the predictor variable

Question 20

Multiple linear regression assumes homo_______

Answer 20

homoscedasticity- residuals stay relatively constant over the range of the predictor variable

Question 21

________ refers to a high similarity between two or more variables.

Answer 21

multicollinearity

Question 22

Singularity refers to a redundant variable. This typically occurs when one variable….

Answer 22

is a combination of two or more other variables. e.g intelligence scales

Question 23

What are we trying to detect if we look for high multivariate correlations?

Answer 23

singularity

Question 24

What are we trying to detect if we look for high bivariate correlations?

Answer 24

multicollinearity

Question 25

Small range of the predictor variable restricts _________

Answer 25

statistical power