Stats - correlation and regression

Question 1

What is correlation used for?

Answer 1

Correlation is used to test for association between variables (e.g. whether salary and IQ are related).

Question 2

How is regression used, and how does it relate to correlation?

Answer 2

Once correlation between two variables has been shown, regression can be used to predict values of other dependent variables from independent variables. Regression is not used unless two variables have firstly been shown to correlate.

Question 3

What are the 3 basic categories of correlation?

Answer 3

Linear
Non-linear
No correlation

Question 4

Variables that are correlated through a linear relationship can display either positive or negative correlation.
What is the difference between these two?

Answer 4

Positively correlated variables vary directly (as one increases so does the other).

Negatively correlated variables vary as opposites (as the value of one variable increases the other decreases).

Question 5

How do you measure the strength of correlation?

Answer 5

The strength of the association can be estimated by observing a scatter graph of the variables. The correlation type is independent of the strength.

It can be strong/ moderate/ weak.

Question 6

How do you measure the strength of a linear relationship?

What symbols are given to the sample and the population correlation coefficients?

Answer 6

Correlation coefficient (Pearson’s correlation coefficient).

The sample correlation coefficient is given the symbol r.

The population correlation coefficient has the symbol ρ (rho).

Question 7

The sign of the correlation coefficient tells us the direction of the linear relationship. How do positive and negative correlations appear?

Answer 7

If r is negative (<0) the correlation is negative and the trend line slopes down. If r is positive (> 0) the correlation is positive and the trend line slopes up.

Question 8

The size (magnitude) of the correlation coefficient tells us the strength of a linear relationship.
What value does r have in a:
1) very strong linear association

Answer 8

r = 0.8-1

Question 9

The size (magnitude) of the correlation coefficient tells us the strength of a linear relationship.
What value does r have in a:
2) strong correlation

Answer 9

0.6-0.79

Question 10

The size (magnitude) of the correlation coefficient tells us the strength of a linear relationship.
What value does r have in a:
3) moderate correlation

Answer 10

0.4-0.59

Question 11

The size (magnitude) of the correlation coefficient tells us the strength of a linear relationship.
What value does r have in a:
4) weak correlation

Answer 11

0.2-0.39

Question 12

The size (magnitude) of the correlation coefficient tells us the strength of a linear relationship.
What value does r have in a:
5) very weak linear association

Answer 12

0-0.19

Question 13

Parametric statistic procedures rely on assumptions about the shape of the distribution.

What 3 characteristics do parametric data assume?

Answer 13

1) normal distribution
2) measured on an interval/ ratio scale
3) conditions or groups have equal variance

Question 14

How is a complete absence of correlation expressed?

Answer 14

0

Question 15

How do we summarise correlation using:
a) parametric variables
b) non-parametric variables

What are the symbols for:
c) the samples
d) the population

Answer 15

a) Pearson’s
b) Spearman’s rank

c) parametric - r, non-parametric - rs
d) p (for both)

Question 16

What is linear regression?

Answer 16

In contrast to the correlation coefficient, linear regression may be used to predict how much one variable changes when a second variable is changed. A regression equation may be formed, y = a + bx, where

y = the variable being calculated (predicted value of response variable)
a = the intercept value (value of y when x = 0)
b = the slope of the line or regression coefficient. Simply put, how much y changes for a given change in x
x = the second variable

Question 17

What kind of graph is used in correlation and regression analysis?

What goes on the x and y axis?

Answer 17

Scatter graphs

They assist in determining, visually, if variables are associated. They may also show the nature of a relationship. They can also assist in determining if there are any outliers that may be effecting the distribution.

X-axis = independent variable

Y-axis = dependent variable

Question 18

What are the:
A) dependent variable
B) independent variable

Answer 18

Dependent variable: The variable being measured in an experiment, which depends on the changes in the independent variable (Y axis)

Independent variable: The variable that is manipulated or controlled by the experimenter to observe its effect (x axis)