Regression

Question 1

What is a correlation?

Answer 1

An association or dependency between two independently observed variables

Question 2

What graph/plot can we use to visualise a correlation?

A Bar chart
B Bar Graph
C Q-Q Plot
D Scatterplot

Answer 2

D Scatterplot

Question 3

Pearson correlation co-efficient scores give an r value ranging between -1 and 1,
A score of 0 indicates what?
What does a score of 1 indicate?
What does a score of -1 indicate?
What do positive and negative scores indicate?

Answer 3

0 = no relationship between the variables
1 = Variables are identical
Positive - variables positively correlated
-1 = variables are exactly inverse
negative means variables are negatively correlated

Question 4

If variables are both interval/ratio, we use a ___________ coefficient test, giving us an ___ value

Answer 4

Pearson’s coefficient
r value

Question 5

If both variables are ordinal. we use either a Spearman’s rank, giving us a ____ value, or a Kendall’s rank, giving us a ____ value

Answer 5

Spearman’s = Rho
Kendall’s = tau

Question 6

If both variables are dichotomous (binary), we use a ____coefficient.

Answer 6

phi coefficient

Question 7

If we have one dichotomous variable, and one interval/ratio variable, we use a _____-______ coefficient, giving us an ___ value.

Answer 7

point-biserial coefficient
rpb value

Question 8

A partial correlation is used when we have more than __ variables, and we want to test the _________ of a pair, whilst __________ for another variable.

Answer 8

partial correlation = when more than 2 variables
want to test correlation/association of one pair whilst accounting for a third

Question 9

Multiple linear regressions describe/examine what?

Answer 9

The relationship between one or more predictor variables and a criterion variable

Question 10

True or false, virtually all statistical models we use (ANOVA, t test, correlations) are special cases of the regression model

Answer 10

True

Question 11

The regression line has the equation:

y= ax + b

Where y is the ______, x is the _______, ax is the ____/______, and b is the _-_______

Answer 11

y is height, x is length across
ax = slope, b = y-intercept

Question 11

A residual error is how far a ____ _____ is from the _____ __ ___.

Answer 11

how far data point lies from line of fit

Question 12

SST = ___ + ____

Answer 12

SST = SSR+SSM

Question 13

prediction error is the difference between the ______ value and the _____ value

Answer 13

Pe = difference between prediction value and actual value

Question 14

The best fit of the ____ occurs by minimizing _____ ______

Answer 14

best fit of model occurs by minimising prediction error

Question 15

The coefficient of determination value is represented as ________

Answer 15

R squared

Question 16

The goodness of fit of a model can be assessed using what 3 measures?

Answer 16

Multiple correlation coefficient = R
Coefficient of determination = R squared
F-Ratio

Question 17

Similar to ANOVA , F-rations of regressions compare the ________ variance to the ________ variance or ________ total variance. Higher F-Ratios represent a _____ model and an increased prediction of _______ value - ______ value.

Answer 17

comparing explained variance to residual variance or total variance
higher f ratios = better model
better prediction, of actual value - predicted value

Question 18

In Regressions, we use _____ squares rather than ____ __ squares for F-Ratios.

F = ____/____

Answer 18

use mean squares rather than sum of squares

f = MSm/MSR

Question 19

MSM = ____/____

MSR = ____/____

Answer 19

MSR = SSM/dfM

MSR = SSR/ dfR

Question 20

dfM (degrees of freedom M) is the number of _______ _______

dfR (degrees of freed R) is the number of ____________ minus the number of ________

Answer 20

dfM = number of predictor variables
dfR = number of observations (p’s) - number of coefficients

Question 21

Effect size for regressions use the value of ___________.
A small effect size is a value of ______
A medium effect size is a value of ______
A large effect size is a value of ______

Answer 21

cohens f squared
small effect size = 0.02
medium = 0.15
large = 0.35

Question 22

Cohens f squared = ________/ (_______)

Answer 22

rsquared/ 1-rsquared

Question 23

What are the 3 main types of regressions, how do they each work?

Answer 23

Simultaneous - no a priori - all variables fit together
Stepwise - no a priori - predictor variables are added/removed one at a time
Hierarchical - based on a priori knowledge - create sever models by adding/removing variables each step, compare models to see which explains the best

Question 24

Outliers are points which _______ substantially from others. They can affect the _______ _____ of ______. ______ distance measures the ______ of an outlier, where a value over _ is concerning

Answer 24

outliers = deviatins from other data points
can affect the linear model of fit
cooks distance reveals how bad outliers are, value over 1 is concerning

Question 25

Scedasticity refers to the distribution of the residual error.

What is homoscedasticity, how can it be seen?

What is heteroscedasticity. how can it be seen?

Answer 25

homoscedasticity = distribution of residuals remain constant over range of predictor, no discernable pattern.

heteroscedasticity = distribution of residuals vary systematically, forming a pattern

Question 26

Multicollinearity refers to what? is it good or bad

Answer 26

multicollinearity refers to high similarity between two or more variables - do not want this

Question 27

Singularity refers to a _______ variable. This is when one variable is a _________ of two or more variables or __-______.

Answer 27

singularity refers to redundant variable
when one variable = combo of two subscores/subscales

Question 28

Multicollinearity can be detected using _________ correlations
singularity can be detected using ________ correlations.
Both can also be checked using ________ values

Answer 28

multicollinearity detected with bivariate correlations
singularity tested using multivariate correlations
both can be tested with tolerance values

Question 29

Multicollinearity can be detected from ____ tolerance values

A Low
B High
C Varying
D Similar

Answer 29

A Low

Question 30

The rule of thumb is that number of __________ (N) should be high compared to the number of ________ variables (m).

Answer 30

N should be high compared to number of predictors (M)

Question 31

A small range of the predictor variable ______ statistical power.

Answer 31

restricts statistical power