Multiple Regression

Question 1

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

Answer 1

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).

Question 2

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

Answer 2

ANOVA Table in the SPSS output

Question 3

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

Answer 3

F statistic

Question 4

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

Answer 4

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

Question 5

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

Answer 5

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.

Question 6

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

Answer 6

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

Question 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.

Answer 7

• 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

Question 8

What are the four assumptions of multiple regression?

Answer 8

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.

Question 9

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

Answer 9

1. research design
2. residual plot
3. residual plot
4. residual plot

Question 10

What are the two requirements for this design?

Answer 10

1. Two or more predictor variables

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

Question 11

The stability of regression coefficients is measured with what?

Answer 11

• tolerance
• tolerance= 1-Rk123^2
  L> Rk123^2 refers to the ability of other predictor variables to predict k

Question 12

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

Answer 12

• stability

- vary dramatically

Question 13

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

Answer 13

• more than one!

L> accounts for more variability in Y

Question 14

What does R^2 tell us?

Answer 14

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

Question 15

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

Answer 15

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

Question 16

What is the formula for R^2?

Answer 16

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

Question 17

MR uses IV’s to predict what?

Answer 17

DV

Question 18

What is the MR equation?

Answer 18

y’= b1x1+b2x2+b3x3 + a

y’= DV we are predicting

b= slope

x= raw score

a= intercept

Question 19

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

Answer 19

there wasn’t a lot of error

Question 20

SPSS:(enter method)

L> how do we enter data

Answer 20

separate column for each variable

Question 21

SPSS(enter method)

L>How to start analysis

Answer 21

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)

Question 22

SPSS(enter method)

L> examining the data results (four boxes)

Answer 22

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 +/-

Question 23

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

Answer 23

• 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.

Question 24

SPSS: Forward Method:

L> set up?

Answer 24

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

Question 25

SPSS: Forward Method

L> what is the plot made of?

Answer 25

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

Question 26

SPSS: Forward Method

L> R^2 change=??

Answer 26

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

Question 27

SPSS: Forward Method

If R^2 change = 0.197 describe it!

Answer 27

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

Question 28

SPSS: Forward Method

L> F is used to?

Answer 28

• determine if there is a significant addition of that variable!

Question 29

SPSS: Forward Method

L> Data boxes??

Answer 29

1. box
   L> only keeps predictors that are significant
   ( use the largest to interpret because it will include all significant predictors! )

Question 30

Homoscedasticity?

Answer 30

• error/variance is relatively the same across the regression line!

Question 31

Linearity?

Answer 31

regression is a straight line!

L> relationship between criterion variable and predictor variable is linear when other predictors are held constant!