Correlation & Regression
What is r equal to? (the inequality)
-1<r<1
What does covariance depend on?
The SCALE of the variable.
What is the difference between variance and covariance?
Covariance deals with TWO variables! Variance deals only with one variable.
What's the difference between covariance and correlation?
Covariance is NOT standardized. Correlation IS standardized.
What is regression?
Describes the form or function of the linear relationship between x & y
How would you standardize the covariance?
Dividing the covariance by the SD of each variable
True or false: Correlation implies causation.
FALSE, DUDE!
What does a regression do?
Forms a prediction equation to predict Y from X
How do you get strong associations through covariance?
Strong associations result from many matches Weak associations result from few matches
What kind of relationship do you have if the size of correlation is between: .6 to .8
Strong relationship
Definition of correlation:
The degree of linear relationship between X & Y
What does covariance capture?
The linear association between two variables
What does r measure?
The positive or negative relationship. Measures only the DEGREE of linear relationship.
What is regression "concerned" with?
The prediction of Y from X
What does r squared represent?
The proportion of variability in Y that is explained by X
What does r squared tell us?
The proportion of variability that is accounted for. That is, the variability in X that is explained by Y.
What can covariance be thought of as?
The sum of the matches and mismatches across participants. MATCH : both variables are on the same side of the mean MISMATCH: The score on one variable is above the mean, but the score on the other variable is below the mean
What is the purpose of correlation/regression?
To help us understand the RELATIONSHIPS between variables. How the value of one variable changes when the value of another variable changes.
If X or Y has zero spread, then r is...
UNDEFINED
What kind of relationship do you have if the size of correlation is between: .8 to .1
Very strong relationship
What kind of relationship do you have if the size of correlation is between: .2 to .4
Weak relationship
Would the correlation be the same for variables on a 1-7 scale as variables on a 1-100 scale?
YES.
Can you name either axis x or y?
Yes. They are statistically interchangeable, BUT there are often conceptual reasons for why you would put on as X and the other as Y.
What does correlation reflect of the linear relationship?
the DEGREE and the DIRECTION
What is covariance a measure of?
the DIRECTION and MAGNITUDE of the linear association between X & Y
What kind of relationship do you have if the size of correlation is between: .0 to .2
weak or no relationship
What does correlation range from? Does scale matter?
-1 to 1, regardless of the scales of the variables involved
If all the scores are on one line in a distribution (though not a vertical/horizontal line)- then what is your corr. coefficient?
1 or -1
What are the two parts of the formula for correlation (with the square roots, not z-score formula)?
1. Measure the linear association between two variables (numerator) 2. Standardizing process (denominator)
What two pieces of information do you get from the correlational coefficient?
1. Numeric value: how strong the association is 2. Positive or negative association
What is r the measurement of?
A measurement of the effect size- the magnitude of the effect
What WILL N affect if not the r?
It will affect the p-value.
Which has a larger covariance: variables on a 1-7 scale or variables on a 1-100 scale?
Larger covariance on the 1-100 scale
What do correlation and regression BOTH examine?
Linear (straight line) relationships
What kind of relationship do you have if the size of correlation is between: .4 to .6
Moderate relationship
Is r affected by N?
NO
Does an ANOVA allow us to make assumptions about causation?
NO.
Does the correlation coefficient tell us about slope?
NO.
Is correlational research experimental?
NO.
Does correlation reflect aspects of nonlinear relationships?
NO. It does not "see" a non-linear relationship. No curvilinear relationships.
What kind of correlation do you have if: x decreases in value and y increases in value?
Negative
What kind of scores does correlation work with?
Pairs of scores! One score on each of the two variables (x & y)
What kind of correlation do you have if X decreases and Y decreases?
Positive
What kind of correlation do you have if: y increases in value and x increases in value?
Positive
What is "r" called?
The Pearson product correlation coefficient
What is the definitional formula for r?
The average product of z scores for X & Y
What is r squared known as?
The coefficient of determination!
What is the OTHER formula for a correlation? (NOT the one with the z-scores)
cov (x, y) ___________ sq root of Var x * sq root of Var y
What is correlation? What does it refer to?
it's a statistical technique that is used to analyze data
What statistic is correlation measured by?
r
What is the formula for r?
r = EZ1*Z2 _________ N-1
If a z score's SD is 0, what is r?
r is undefined, because in order to calculate a z score, you must have variability! So, the calculation for r falls apart!
What will the value of r be if there is NO linear relationship between X & Y?
r=0
If r=.7, what is r squared?
r^2 = .49, which accounts for about half of the variability.
If r=.9, what is r squared?
r^2 = .81, which accounts for almost all the variability (81%)