Chapters 32 and 33: Correlation and Regression

Question 1

What does correlation do?

Answer 1

It quantifies the association between two continuous variables.

Question 2

How do you find the coefficient of variation?

Answer 2

Divide the Standard Deviation by the mean

Question 3

Does the coefficient of variation have units?

Answer 3

No

Question 4

What is the coefficient of variation useful for?

Answer 4

It is useful for comparing the Standard Deviation to the mean and for comparing the scatter of variables measured in different units.

Question 5

What is another term for correlation?

Answer 5

Covariation

Question 6

What does the Correlation Coefficient (r) measure?

Answer 6

It measures the direction and magnitude of the linear correlation.

Question 7

What are the values for the Correlation Coefficient?

Answer 7

-1 to 1

Question 8

What does zero mean in regard to the Correlation Coefficient?

Answer 8

Zero means no correlation

Question 9

What does a positive Correlation Coefficient mean?

Answer 9

It means the variables increase or decrease together.

Question 10

What does a negative Correlation Coefficient mean?

Answer 10

It means the variables are inversely related.

Question 11

In regard to the Correlation Coefficient, what does a 95% CI mean?

Answer 11

It means there is a 95% chance that the CI (of r) includes the population correlation coefficient.

Question 12

The CI is not symmetrical unless…why?

Answer 12

the r=0 because r cannot be greater than 1.0 or

Question 13

When is the Correlation Coefficient more symmetrical?

Answer 13

When the CI is large.

Question 14

What is r squared?

Answer 14

The fraction of the variance shared between the two variables.

Question 15

In correlation, what is the null hypothesis?

Answer 15

The null hypothesis is that there is no correlation.

Question 16

What does r squared mean?

Answer 16

It’s the effect size for correlation.

Question 17

What do r squared values indicate?

Answer 17

They indicate the amount of variation shared or explained.

Question 18

What assumptions are made with correlations?

Answer 18

-Random, independent observations
-Normal distributions (of X and Y values).
• Paired (X & Y) observations from one population
• Assumes all covariation is linear
• Or won’t be detected if nonlinear
-No outliers
• X values are not experimentally controlled.

Question 19

Describe what the Spearman correlation is.

Answer 19

It is a rank-based nonparametric test that is similar to a

Pearson’s correlation test.

Question 20

What are the steps and rules for a Spearman correlation test?

Answer 20

1. Separately rank X and Y values.

2. Perform the same steps as a Pearson correlation test but with the ranks.

Question 21

What are the benefits of a Spearman correlation test?

Answer 21

It doesn’t assume a Gaussian distribution and it doesn’t suffer from outliers.

Question 22

What does linear regression determine?

Answer 22

It determines the best linear model to represent the causal relationship between X and Y.

Question 23

What is the X variable in linear regression?

Answer 23

The independent variable

Question 24

What is the Y variable in linear regression?

Answer 24

The dependent variable

Question 25

How does linear regression fit?

Answer 25

``` Linear regression fits the ‘best fit line’ through a graph of data points. ```

Question 26

Line equation:

Answer 26

Y = mX + b

Question 27

Linear regression must also account for...

Answer 27

variability

Question 28

What does linear regression not do?

Answer 28

It does not find the line that comes closest to the points on the graph.

Question 29

What does linear regression minimize?

Answer 29

It minimizes the vertical distances (residuals) of the points from the line.

Question 30

What does correlation assume?

Answer 30

``` Correlation assumes a linear relationship in which both X and Y values exhibit error. ```

Question 31

What does linear regression assume?

Answer 31

``` Linear regression assumes that X values are measured without error, but all of the error exists in Y ```

Question 32

In either correlation or linear regression, what does the best fit line minimize?

Answer 32

The sum of the squared distances between the line and all of the points

Question 33

Why is this a squared distance?

Answer 33

It is a squared distance because doing that finds the best midpoint between points.

Question 34

What are we using in order the estimate the best linear model?

Answer 34

The values of the parameters of the linear model

Question 35

What is the null hypothesis for simple linear regression?

Answer 35

The null hypothesis states that the line of best fit has a slope of 0.

Question 36

What is the essentially equivalent to?

Answer 36

Essentially equivalent to the null of no correlation.

Question 37

The P values for linear regression and correlation are...

Answer 37

identical.