Multiple Regression Flashcards

1
Q

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

A

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).

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2
Q

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

A

ANOVA Table in the SPSS output

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3
Q

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

A

F statistic

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4
Q

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

A

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

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5
Q

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

A

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.

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6
Q

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

A

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

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7
Q

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.

A
  • 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
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8
Q

What are the four assumptions of multiple regression?

A
  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.
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9
Q

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

A
  1. research design
  2. residual plot
  3. residual plot
  4. residual plot
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10
Q

What are the two requirements for this design?

A
  1. Two or more predictor variables

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

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11
Q

The stability of regression coefficients is measured with what?

A
  • tolerance
  • tolerance= 1-Rk123^2
    L> Rk123^2 refers to the ability of other predictor variables to predict k
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12
Q

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

A
  • stability

- vary dramatically

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13
Q

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

A
  • more than one!

L> accounts for more variability in Y

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14
Q

What does R^2 tell us?

A

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

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15
Q

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

A

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

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16
Q

What is the formula for R^2?

A

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

17
Q

MR uses IV’s to predict what?

A

DV

18
Q

What is the MR equation?

A

y’= b1x1+b2x2+b3x3 + a

y’= DV we are predicting

b= slope

x= raw score

a= intercept

19
Q

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

A

there wasn’t a lot of error

20
Q

SPSS:(enter method)

L> how do we enter data

A

separate column for each variable

21
Q

SPSS(enter method)

L>How to start analysis

A

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
Q

SPSS(enter method)

L> examining the data results (four boxes)

A
  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
Q

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

A
  • 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
Q

SPSS: Forward Method:

L> set up?

A
  • same as the enter method except now you pick forward instead of enter for the model.
25
Q

SPSS: Forward Method

L> what is the plot made of?

A
  • z-residual on Y and z predicted on x axis!
26
Q

SPSS: Forward Method

L> R^2 change=??

A

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
Q

SPSS: Forward Method

If R^2 change = 0.197 describe it!

A

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

28
Q

SPSS: Forward Method

L> F is used to?

A
  • determine if there is a significant addition of that variable!
29
Q

SPSS: Forward Method

L> Data boxes??

A
  1. box
    L> only keeps predictors that are significant
    ( use the largest to interpret because it will include all significant predictors! )
30
Q

Homoscedasticity?

A
  • error/variance is relatively the same across the regression line!
31
Q

Linearity?

A

regression is a straight line!

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