Chapter 14: Correlation and Regression

Question 1

correlation

Answer 1

A statistical method used to measure and describe the relationship between two variables

Question 2

when do correlations exist

Answer 2

when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable

Question 3

what three aspects of a relationship do correlation measure?

Answer 3

the direction, form, and strength

Question 4

positive correlation

Answer 4

two variables change in the same direction

Question 5

negative correlation

Answer 5

two variables change in opposite directions

Question 6

correlation coefficient

Answer 6

Measured by a value ranging from 0.00-1.00, where 0 is no correlation and 1 is a perfect correlation

Question 7

what types of data use the Pearson correlation?

Answer 7

data having linear relationships
data from interval or ratio measurement scales

Question 8

what type of data uses spearman correlation?

Answer 8

used with data from an ordinal scale (ranks)

Question 9

what type of data uses point biserial correlation?

Answer 9

data where one variable is dichotomous and the other consists of regular numerical scores (interval or ratio scale)

Question 10

when is phi-coefficient used?

Answer 10

when you have two dichotomous variables

Question 11

pearson correlation formula

Answer 11

r= covariability of x and y (sp)/ variability of x and y separately (sqrt SSx*SSy)

Question 12

covariation of x and y

Answer 12

sum of (x-mx)(y-my)

Question 13

pearson correlation z-score formula (sample)

Answer 13

r= sum zx zy/ n-1

Question 14

pearson correlation z-score formula (population)

Answer 14

p= sum zx zy/ n

Question 15

uses of the pearson correlation

Answer 15

Used for prediction, validity, reliability, and theory verification

Question 16

correlation doesn’t equal

Answer 16

causation

Question 17

correlation and restricted range of scores

Answer 17

Severely restricted range may provide a very different correlation than would a broaden range of scores
Usually a smaller correlation

Question 18

outlier

Answer 18

deviant individual in the sample

Question 19

correlations and outliers

Answer 19

Outliers provide a disproportionately large impact on the correlation coefficient

Question 20

coefficient of determination

Answer 20

Measures the proportion of variability in one variable that can be determined from the relationship with another variable (r²)

Question 21

non-directional Pearson’s correlation hypotheses

Answer 21

H0: ρ = 0 and H1: ρ ≠ 0

Question 22

positive correlation hypotheses

Answer 22

H0: ρ ≤ 0 and H1: ρ > 0

Question 23

negative correlation hypotheses

Answer 23

H0: ρ ≥ 0 and H1: ρ < 0

Question 24

degrees of freedom for correlation hypothesis tests

Answer 24

n-2

Question 25

Correlation Hypothesis Test formula

Answer 25

t= r-p / sqrt (1-r)2/ n-2

Question 26

How to Test if the Correlation is Different from 0

Answer 26

Convert your correlation to a t-value and use the t-table

Question 27

regression

Answer 27

a method of finding an equation describing the best-fitting line for a set of data that aren’t perfectly related

Question 28

reasons for regression

Answer 28

Make the relationship easier to see Show the central tendency of the relationship Predict y-values for given x-values

Question 29

general equation for regression

Answer 29

y= bx+ a, where X and Y are variables, a is the intercept and b is the slope

Question 30

best regression line

Answer 30

the one that minimizes the prediction error

Question 31

Ŷ

Answer 31

the value of y predicted bt the regression line for each value of x

Question 32

(Y-Ŷ)

Answer 32

the distance each data point is from the regression line (the error of predictor or residual)

Question 33

Least-squared error solution

Answer 33

a line that minimizes the total squared error of prediction

Question 34

how is the regression line calculated?

Answer 34

can be calculated with the components of the correlation coefficient

Question 35

slope formula

Answer 35

b= SP/ SSx OR b= r sy/sx

Question 36

y-intercept formula

Answer 36

a= My- b (Mx)

Question 37

what does a perfect correlation mean?

Answer 37

there is no residual/error

Question 38

standard error of estimate

Answer 38

how much on average do we expect our predictions to be off?

Question 39

what happens to SEoE as r becomes stronger (0 to 1 or -1)

Answer 39

SEoE decreases to 0

Question 40

effect of stronger correlations on the standard error of estimate

Answer 40

will result in fewer errors of prediction

Question 41

predicted variability in y scores

Answer 41

SSregression = r² SSY

Question 42

unpredicted variability in y scores

Answer 42

SSresidual = (1 − r²) SSY

Question 43

Standard Error of Estimate based on r formula

Answer 43

SEoE= √(1-r²)SSY/ (n-2)

Question 44

what happens to the regression slope if you standardize scores into z-scores

Answer 44

it is equal to the correlation coefficient

Question 45

calculating a regression equation from a correlation

Answer 45

Calculate b (slope) Use b value to calculate a (y-intercept)