Correlation and Bivariate Regression

Question 1

Correlation

Answer 1

Used to quantify the degree of relationship, or association, between two variables; the extent to which the direction and size of deviations from the mean in one variable are related to the direction and size of deviations from the mean in another variable

Question 2

Coefficient

Answer 2

(or number) that represents the correlation will always be between +1.00 and −1.00.

Question 3

Perfect Positive Correlation

Answer 3

+1.00; would exist if every subject varied an equal distance from the mean in the same direction (measured by a Z score) on two variables; if every subject who was 1 Z score above the mean on variable X was also 1 Z score above the mean on variable Y, and every other subject showed a similar relationship between deviation score on X and deviation score on Y

Question 4

Perfect Negative Correlation

Answer 4

If all subjects who were above or below the mean on variable X were an equal distance in the opposite direction from the mean on variable Y, the result-ing correlation would be −1.00.

Question 5

A correlation coefficient of 0.00 means that…

Answer 5

No relationship exists between the variables

Question 6

Positive correlations result when…

Answer 6

Subjects who receive high numerical scores on

one variable also receive high numerical scores on another variable.

Question 7

Negative correlations result when…

Answer 7

scores on one variable tend to be high num-bers and scores on a second variable tend to be low numbers.

Question 8

Why is correlation useful?

Answer 8

Measure reliability by comparing test–retest measures on a group of subjects to determine consistency of performance.

Question 9

When the correlation coefficient between two variables is known…

Answer 9

Scores on the second variable can be predicted based on

Question 10

Cause and effect may be present…

Answer 10

but correlation does not prove causation (scores from the first variable. does not indicate the cause of that relationship)

Question 11

Scatter Plot

Answer 11

A visual description of a correlation coefficient; the scores for each subject on two variables are plotted with one variable on the X-axis and the other variable on the Y-axis.

Question 12

Best Fit Line

Answer 12

Represents the best linear estimate of the relationship between the two variables; If the correlation was a perfect +1.00 or −1.00, all of the plotted points would fall exactly on the line. As the correlation approaches 0.00, the data points drift further away from the line until the data points form a random cloud of points.

Question 13

Correlation Coefficient

Answer 13

represents the relationship between the Z scores of the subjects on two variables (usually designated X and Y).

Question 14

Pearson’s product moment correlation coefficient (r) Formula

Answer 14

r = Σ(ZxZy)/N

Question 15

Residuals

Answer 15

The vertical distance from any point to the line;will be positive and negative and the sum of residuals will be equal to zero (in the same way that the sum of the deviation scores from the mean sum to zero).

Question 16

Homoscedasticity

Answer 16

Means that the variance of the residuals does not vary

Question 17

Heteroscedasticity

Answer 17

If the variance of the residuals is not constant

Question 18

If the correlation is high and positive…

Answer 18

a person is likely to score high on both variables, or low on both variables, or in the middle on both variables.

Question 19

If the correlation is high and negative…

Answer 19

a person will tend to score high on one variable and low on the other.

Question 20

Regression

Answer 20

Often used to predict one variable from the value of another.

Question 21

When deciding to use prediction, we must determine whether it is more acceptable to…

Answer 21

tolerate the error in the prediction or the difficulty of direct measurement.