Correlation and Regression

Question 1

What is correlation?

Answer 1

used to determine the relationship between variables or factors

Question 2

What is the correlation coefficient?

Answer 2

a measure of the degree of relationship between 2 variables or two sets of scores

Question 3

If the points on a scatterplot graph almost form a straight line, this means ….

Answer 3

there is a correlation

Question 4

If one variable increases as does the other variable, this means the correlation is _____.

Answer 4

positive

Question 5

Trend line slanting up to the right means the correlation is _______.

Answer 5

positive

Question 6

If one variable increases while the other variable decreases, this means the correlation is _______.

Answer 6

negative

Question 7

Trend line slanting down to the right means the correlation is _______.

Answer 7

negative

Question 8

Correlation is always a number between ______ and ______.

Answer 8

-1.00 and +1.00

Question 9

+1.00 correlation indicates…

Answer 9

• a perfect correlation
• a perfect positive relationship or correspondence
• all dots are co-linear

Question 10

-1.00 correlation indicates …

Answer 10

• a perfect negative correlation
• inverse relationship between the two sets of scores
• all dots are co-linear

Question 11

-0.0 correlation indicates …

Answer 11

• no correlation or relationship

- flat line with no slope

Question 12

Correlations are shown by …

Answer 12

• correlation coefficients

- p or r

Question 13

Correlations can be but are not necessarily _____ and _____.

Answer 13

cause and effect

Question 14

Give an example of when correlation is cause and effect.

Answer 14

• Leg Strength and Sprint Speed

- they are related and one probably causes the other to be true.

Question 15

Give an example of when correlation is not cause and effect.

Answer 15

• Caffeine Consumption and Grades
• they may be a high correlation, but drinking lots of coffee does not necessarily give you good grades
• It may give you the ability to study long hours but the grades are not the direct result of the coffee

Question 16

What are the words used to categorize correlation coefficient?

Answer 16

• excellent
• high
• average
• unacceptable

Question 17

What is the range for excellent correlation coefficient?

Answer 17

±.90 to ±1.00

Question 18

What is the range for high correlation coefficient?

Answer 18

±.80 to ±.89

Question 19

What is the range for average correlation coefficient?

Answer 19

±.60 to ±.79

Question 20

What is the range for unacceptable correlation coefficient?

Answer 20

< ±.59

Question 21

Spearman rho rank order correlation coefficient is the one where we ….

Answer 21

• re-create the table with all the columns

- write your own formula since excel does not have a function for this

Question 22

To determine the rank order correlation coefficient, the steps are:

Answer 22

1. the scores fro each variables are listed and ranked
2. the difference in ranks is determined
3. the difference in ranks is squared

Question 23

If scores are identical when using the spearman rho correlation coefficient method, those tied scores are given ….

Answer 23

the mean value of the number of tied ranks

Question 24

Ex. what if 3 scores are tied in rank for 2, 3, and 4th place?

Answer 24

• add up 2+3+4
• 9/3
• each one has a rank of 3

Question 25

Ex. what if 2 scores are tied in rank for 3rd and 4th place?

Answer 25

- add up 3+4 - 7/2 - each one has a rank for 3.5

Question 26

Pearson correlation coefficient is the one where we...

Answer 26

- create a table in excel with the raw scores only (x and y columns) - use the =CORRELATION formula in excel

Question 27

Which method of calculating correlation coefficients is more accurate?

Answer 27

Pearson correlation coefficient

Question 28

How do we check the "goodness" of a correlation coefficient?

Answer 28

coefficient of determination

Question 29

What does the coefficient of determination do?

Answer 29

- theoretical approximation of the amount of similar quantities found in the two variables being compared

Question 30

How is the coefficient of determination calculated?

Answer 30

- squaring the correlation coefficient | - p^2 or r^2

Question 31

If the coefficient of determination is 0.81, this means ...

Answer 31

81% of whatever makes this person ____ is also responsible for making him _____

Question 32

The "whatever makes this person _____" of interpreting the coefficient of determination could be a composite of factors such as:

Answer 32

- strength - explosive power - reaction time - desire to win

Question 33

What is regression?

Answer 33

- used to show relationship | - predict or determine the performance of a variable from another variable

Question 34

Why is regression or prediction important in the development of many tests in physical education?

Answer 34

can predict a variable that is difficult to measure

Question 35

Give an example of how regression can be used in a test for physical education.

Answer 35

- max VO2 testing requires expensive lab equipment and lots of time - regression equation for predicting VO2 from scores on a 12 minute run is used

Question 36

The stronger the correlation between the 2 variables...

Answer 36

the better the regression equation will be at predicting

Question 37

When the regression formula is graphed, it forms ...

Answer 37

the line of best fit

Question 38

What is the regression equation?

Answer 38

y = mx + b

Question 39

What is y?

Answer 39

represents the variable we want to determine (predict)

Question 40

What is x?

Answer 40

represents the variable score used to predict y

Question 41

What is m?

Answer 41

- represents the amount of change in y associated with each unit change in x - aka slope - indicates if the relationship is positive or negative

Question 42

What is b?

Answer 42

- represents the constant adjustment that must be made in order to put x and y on the same scale - aka y-intercept of the line