Correlation + Regression

Question 1

Similarities between correlation and regression

Answer 1

• Both analyze relationships between variables, but they differ in their purpose and interpretation.

Question 2

Differences between correlation and regression

Answer 2

• Correlation measures the strength and direction of a linear relationship between two variables, represented by a single value between -1 and 1
• Regression, on the other hand, explores how one variable influences another, providing an equation that describes the relationship and allows for prediction; SUSPECTED OR LOGICAL DIRECTION

Question 3

What does regression allow us to do?

Answer 3

Allows us to add predictors to explain more variance

Question 4

On a chart, what are the x and y labels

Answer 4

• Criterion on Y
• Predictor on X

Question 5

The average (squared) deviation from each person’s score Y to their predicted score Y(hat) is called the…

Answer 5

STANDARD ERROR OF THE ESTIMATE

Question 6

Regression Equation - UNSTANDARDIZED VERSION:

Answer 6

• Uses raw scores
• Y(hat) = a + bX
• For multiple predictors: add on more bX

Question 7

Regression Equation - UNSTANDARDIZED VERSION: B

Answer 7

B = r(SDy/SDx)

Question 8

How can we interpret “b”?

Answer 8

For every one unit change in X, predict a b unit change in Y

Question 9

Regression Equation - UNSTANDARDIZED VERSION: A

Answer 9

A = My - b(Mx)

Question 10

Where can we find “a” in SPSS?

Answer 10

“CONSTANT”

Question 11

How can we interpret “a”?

Answer 11

The predicted score on Y when the X = 0

Question 12

Regression Equation - STANDARDIZED VERSION:

Answer 12

• SAME - but uses z scores
• Z(sub y hat) = BetaZx
• For multiple predictors: add on more betas
• Predicted score on Y when X = 0 is always 0 when both variables are z scores, because the mean of both sets of z scores is 0
• USE: if given someone’s z score(s) on predictor variables, use the standardized equation

Question 13

Which component of the SPSS output do we use for the unstandardized regression equation?

Answer 13

UNSTANDARDIZED COEFFICIENTS

Question 14

Which component of the SPSS output do we use for the standardized regression equation?

Answer 14

STANDARDIZED COEFFICIANTS

Question 15

How do we report the null hypothesis for correlation?

Answer 15

H0 : ρ = 0

Question 16

MULTIPLE REGRESSION

Question 17

What is multiple regression asking?

Answer 17

How well can we predict scores on Y using two (or more) predictor variables

Question 18

Multiple regression UNSTANDARDIZED equation

Answer 18

Y(hat) = a + b1X1 + b2X2

Question 19

What does b1 and b2 represent?

Answer 19

• how well does variable X1 predict scores on Y, independent of X2
• how well does variable X2 predict scores on Y, independent of X1

Question 20

What does R2 represent in relation to b1 and b2

Answer 20

R2: how well do both of these predictors, combined, predict scores on Y

Question 21

Multiple regression STANDARDIZED equation

Answer 21

• Z(hat)y = B1Zx1 + B2Zx2
• NOTE: B = beta

Question 22

How can we interpret the UNSTANDARDIZED multiple regression coefficient

Answer 22

• For every one score increase in ___, predict a ____(constant) increase in ____, holding constant the effect of ____ (the other b)

Question 23

How can we interpret the STANDARDIZED multiple regression coefficient

Answer 23

For every one standard deviation increase in ___, predict a ____(constant) increase in ____, holding constant the effect of ____ (the other Zx2)