Correlation and Regression Flashcards
What is correlation?
used to determine the relationship between variables or factors
What is the correlation coefficient?
a measure of the degree of relationship between 2 variables or two sets of scores
If the points on a scatterplot graph almost form a straight line, this means ….
there is a correlation
If one variable increases as does the other variable, this means the correlation is _____.
positive
Trend line slanting up to the right means the correlation is _______.
positive
If one variable increases while the other variable decreases, this means the correlation is _______.
negative
Trend line slanting down to the right means the correlation is _______.
negative
Correlation is always a number between ______ and ______.
-1.00 and +1.00
+1.00 correlation indicates…
- a perfect correlation
- a perfect positive relationship or correspondence
- all dots are co-linear
-1.00 correlation indicates …
- a perfect negative correlation
- inverse relationship between the two sets of scores
- all dots are co-linear
-0.0 correlation indicates …
- no correlation or relationship
- flat line with no slope
Correlations are shown by …
- correlation coefficients
- p or r
Correlations can be but are not necessarily _____ and _____.
cause and effect
Give an example of when correlation is cause and effect.
- Leg Strength and Sprint Speed
- they are related and one probably causes the other to be true.
Give an example of when correlation is not cause and effect.
- 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
What are the words used to categorize correlation coefficient?
- excellent
- high
- average
- unacceptable
What is the range for excellent correlation coefficient?
±.90 to ±1.00
What is the range for high correlation coefficient?
±.80 to ±.89
What is the range for average correlation coefficient?
±.60 to ±.79
What is the range for unacceptable correlation coefficient?
< ±.59
Spearman rho rank order correlation coefficient is the one where we ….
- re-create the table with all the columns
- write your own formula since excel does not have a function for this
To determine the rank order correlation coefficient, the steps are:
- the scores fro each variables are listed and ranked
- the difference in ranks is determined
- the difference in ranks is squared
If scores are identical when using the spearman rho correlation coefficient method, those tied scores are given ….
the mean value of the number of tied ranks
Ex. what if 3 scores are tied in rank for 2, 3, and 4th place?
- add up 2+3+4
- 9/3
- each one has a rank of 3
Ex. what if 2 scores are tied in rank for 3rd and 4th place?
- add up 3+4
- 7/2
- each one has a rank for 3.5
Pearson correlation coefficient is the one where we…
- create a table in excel with the raw scores only (x and y columns)
- use the =CORRELATION formula in excel
Which method of calculating correlation coefficients is more accurate?
Pearson correlation coefficient
How do we check the “goodness” of a correlation coefficient?
coefficient of determination
What does the coefficient of determination do?
- theoretical approximation of the amount of similar quantities found in the two variables being compared
How is the coefficient of determination calculated?
- squaring the correlation coefficient
- p^2 or r^2
If the coefficient of determination is 0.81, this means …
81% of whatever makes this person ____ is also responsible for making him _____
The “whatever makes this person _____” of interpreting the coefficient of determination could be a composite of factors such as:
- strength
- explosive power
- reaction time
- desire to win
What is regression?
- used to show relationship
- predict or determine the performance of a variable from another variable
Why is regression or prediction important in the development of many tests in physical education?
can predict a variable that is difficult to measure
Give an example of how regression can be used in a test for physical education.
- 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
The stronger the correlation between the 2 variables…
the better the regression equation will be at predicting
When the regression formula is graphed, it forms …
the line of best fit
What is the regression equation?
y = mx + b
What is y?
represents the variable we want to determine (predict)
What is x?
represents the variable score used to predict y
What is m?
- represents the amount of change in y associated with each unit change in x
- aka slope
- indicates if the relationship is positive or negative
What is b?
- 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
