Unit 11 Correlation vs Regression

Question 1

Correlation Analysis examines..

Answer 1

The strength (intensity) of the relationship between two experimental variables.

Question 2

Two things correlation analysis assesses

Answer 2

If the amount of variation in one variable is explained by another variable
If the explained variation is greater than can be expected by chance alone, ie. is it significant

Question 3

Regression Analysis…

Answer 3

Measures the form of the relationship and describes
the functional relationship between variables

Question 4

Where does regression usually apply

Answer 4

Applies when we have control of the X variable
(independent) and can measure it essentially without error

Question 5

the centroid is…

Answer 5

The equivalent of the mean for a double statistical series

Question 6

The covariance is

Answer 6

The covariance between X and Y (Sxy) is the equivalent to the variance (S) for a double statistical series
(two continuous variables, X and Y)

Question 7

What does covariance describe

Answer 7

Describes the dispersion of two or more quantitative variables
Is symmetric: The covariance Sxy equals covariance Sxy(Diagonally)
❑ Variances are always positive (squared)
❑ Covariances can be negative: vary from -∞ to + ∞

Question 8

Variance is…

Answer 8

Covariance matrix or dispersion matrix (dispersion around the mean) (S matrix)

Question 9

Covariance measures…

Answer 9

Covariance measures the joint dispersion of two quantitative variables around their centroid

Question 10

Correlation is…

Answer 10

Correlation is a statistical technique used to determine the degree to which two variables are related

Question 11

Two correlation coefficients are considered:

Answer 11

Pearson product moment correlation coefficient (r)
employed with interval or ratio scaled variables (parametric)
Spearman rank order correlation coefficient (r rho) employed with ordinal or ranked data (non-parametric)

Question 12

Pearson Correlation Coefficient (rxy) measures

Answer 12

Only the linear relationship between two quantitative variables
It is the covariance of standardized variables

Question 13

In correlation a positive relationship means…

Answer 13

Means that ‘individuals’ obtaining high scores on one variable tend to obtain high scores on a second variable.
The converse is also true, i.e. individuals scoring low on one variable tend to score low on a second variable.

Question 14

In correlation a negative relationship means…

Answer 14

Means that ‘individuals’ scoring low on one variable tend to score high on a second variable
Conversely, individuals scoring high on one variable tend to score low on a second variable

Question 15

Residuals is..

Answer 15

The distance between points and what you are measuring.
They are the error terms.
If there are small residuals then there is strong a correlation.

Question 16

The total variance of y can be partitioned in:

Answer 16

1. explained variance
2. residual variance

Question 17

Linear regression is:

Answer 17

Linear regression is a form of statistical modelling (we are predicting the future)

Question 18

Linear regression can aim to:

Answer 18

Describe a functional model linking y and x
Test hypothesis regarding model parameters.
Predict y as a function of y.

Question 19

How to quantify correlation between variables:

Answer 19

Pearson’s correlation coefficient

Question 20

What does Pearson’s Correlation Coefficient assess.

Answer 20

The sign of r denotes the nature of association (positive or negative)
The value of r denotes the strength of the association between (-1) and (+1)
The further r is away from 0 the larger the sample size. So the less likely the association could have occurred by chance if there was no real association between the variables considered.

Question 21

The closer the r value is to 0…

Answer 21

The greater the variation around the line

Question 22

When do we use Pearson r significance test?

Answer 22

To test if a relationship exists between two variables, and determine the magnitude and direction.
To test if two sets of paired measurements, neither of which is clearly independent of the other, are linearly associated.

Question 23

Assumptions of Pearson’s r significance test

Answer 23

For each subject in the study there must be related pairs of scores:
- If a subject has a score on variable x, then the same subject must have a score on variable y.
- The variables must have a linear relationship. ie. the relationship can be most accurately represented by a straight line.

Question 24

Rules for Pearson’s correlation hypothesis testing

Answer 24

• Significance (two-tailed) or p-value > 0.05, reject H0 There is no correlation between the two variables.
• Significance (two-tailed) or p-value ≤ 0.05, reject H0
  Assume there’s linear correlation between the variables. There is a significant association between variables.

Question 25

Word of caution for correlation and causation

Answer 25

Correlation doesn’t imply causation

Question 26

Correlation analysis examines:

Answer 26

the strength (intensity) of a relationship between two variables.

Question 27

Regression analysis measures:

Answer 27

the form of the relationship and describes the functional relationship between variables.
regression usually applies when we have control of the x variable (independent) and can measure it without error.

Question 28

Regression:

Answer 28

While correlation is concerned with the magnitude and direction of the relationship, regression focuses on using the relationship as a prediction model

Question 29

Linear regression is a form of:

Answer 29

Statistical modelling
(we are predicting the future)