Flashcards in Multiple Regression Deck (31):

1

## When is a statistical test for the entire regression equation conducted ?

### when we want to know if the overall regression ( overall regression model ) is significant. This tells us if our predictors (X1, X2,X3 etc) are good predictors of our criterion (Y).

2

## With SPSS this test is conducted within the regression analysis and the results are displayed in what?

### ANOVA Table in the SPSS output

3

## To determine if the overall regression model is significant you interpret the ___ and its associated significance level (sig)

### F statistic

4

## By hand what are the two formulas for calculating statistical significance for multiple regression?

###
Fobt= (SSreg/k)/ (SS res/N-k-1)

or

Fobt=( R^2/k)/(1-R^2)/(N-K-1)

where Df num = k

df denom= N-k-1

5

## Tests for different regression models is done when you want to what?

### determine whether there i s a significant different between a one predictor model and a two predictor model in terms of their ability to predict Y.

6

## With SPSS when you want to test different regression models via regression analysis the results are represented as?

### F statistic that is associated with R^2 change values for adding predictors to the regression model

7

## What is the formula for when we want to calculate an F stat to determine whet ere there is a difference between a one predictor model and a two predictor model etc.

###
- Fobt= (R^2k1-R^2k2)/(k1-k2)/ (1-R^2k1)/(N-K1-1)

where:

k1= larger set of predictors

k2= smaller set of predictors

df num= k1-k2

df denom= N-K1-1

8

## What are the four assumptions of multiple regression?

###
1. Independence of scores

2. normality: scores on criterion variable (y) follow a normal distribution for each combination of predictor variables

3. homoscedasticity

4. linearity: relation between criterion variable and a predictor is linear when other predictors are held constant.

9

## How are the assumptions of multiple regression assessed? (4)

###
1. research design

2. residual plot

3. residual plot

4. residual plot

10

## What are the two requirements for this design?

###
1. Two or more predictor variables

2.N= 50, 10x more subjects than predictors

11

## The stability of regression coefficients is measured with what?

###
- tolerance

- tolerance= 1-Rk123^2

L> Rk123^2 refers to the ability of other predictor variables to predict k

12

## In general, the higher the tolerance, the greater the ___. If tolerance approaches 0, the coefficients can?

###
- stability

- vary dramatically

13

## Multiple regression invokes using one/ or more predictors for the criterion?

###
- more than one!

L> accounts for more variability in Y

14

## What does R^2 tell us?

### the total proportion of variance in Y that is accounted for by the X variables.

15

## R^2 is similar to r^2(simple regression) but it is different in what way?

### combines the proportion of variance accounted for by the x variables combined. Simple regression only invokes one predictor so there is no need to combine anything

16

## What is the formula for R^2?

### R^2= ryx1^2 +ryx2^2 - 2ryx1ryx2rx1x2/ 1- rx1x2^2

17

## MR uses IV's to predict what?

### DV

18

## What is the MR equation?

###
y'= b1x1+b2x2+b3x3 + a

y'= DV we are predicting

b= slope

x= raw score

a= intercept

19

## If there is a small difference between the predicted and the actual value this indicates what?

### there wasn't a lot of error

20

##
SPSS:(enter method)

L> how do we enter data

### separate column for each variable

21

##
SPSS(enter method)

L>How to start analysis

###
analyze----regression------linear

L> y goes into DV and x's go into IV

L> click statistics: estimates, model fit and r squared change

L> method box: enter ( use all x's at once)

22

##
SPSS(enter method)

L> examining the data results (four boxes)

###
1. box

L> what type of regression was done

2. box

L> R value runs -1 to 1....; 0 = no relationship... (gives strength and direction go relationship)

L> R ^2 value accounts for proportion of Y covered by X ...higher the better

L> adjusted R^2= USE IT...accounts for type 1 error

3. box: ANOVA

L> tells us if entire regression was sig

L> interpret as a usual anova

p if sig keep reading results! if not stop here.

4. coefficients box

L> shows us which X's were good predictors individually

L> uses t test

L> sig p a = constant variable....B can be +/-

23

## What do the b coefficients tell us from the SPSS data?

###
- The b's tell us that for every 1 unit increase in the IV, a ___ unit decrease/increase in the DV can be expected holding other IV's fixed.

ex: For every 1 unit increase in number of courses a 0.618 unit increase in the exam grade can be expected holding other IV's fixed.

24

##
SPSS: Forward Method:

L> set up?

### - same as the enter method except now you pick forward instead of enter for the model.

25

##
SPSS: Forward Method

L> what is the plot made of?

### - z-residual on Y and z predicted on x axis!

26

##
SPSS: Forward Method

L> R^2 change=??

### difference between the different types of models....difference in Y accounted for by X from the addition of X2 (not accounting for both variables!

27

##
SPSS: Forward Method

If R^2 change = 0.197 describe it!

### 19.17% more of the variance of Y is accounted for by that variable.

28

##
SPSS: Forward Method

L> F is used to?

### - determine if there is a significant addition of that variable!

29

##
SPSS: Forward Method

L> Data boxes??

###
1. box

L> only keeps predictors that are significant

( use the largest to interpret because it will include all significant predictors! )

30

## Homoscedasticity?

### - error/variance is relatively the same across the regression line!

31