Multiple Regression Flashcards
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).
With SPSS this test is conducted within the regression analysis and the results are displayed in what?
ANOVA Table in the SPSS output
To determine if the overall regression model is significant you interpret the ___ and its associated significance level (sig)
F statistic
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
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.
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
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
What are the four assumptions of multiple regression?
- Independence of scores
- normality: scores on criterion variable (y) follow a normal distribution for each combination of predictor variables
- homoscedasticity
- linearity: relation between criterion variable and a predictor is linear when other predictors are held constant.
How are the assumptions of multiple regression assessed? (4)
- research design
- residual plot
- residual plot
- residual plot
What are the two requirements for this design?
- Two or more predictor variables
2. N= 50, 10x more subjects than predictors
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
In general, the higher the tolerance, the greater the ___. If tolerance approaches 0, the coefficients can?
- stability
- vary dramatically
Multiple regression invokes using one/ or more predictors for the criterion?
- more than one!
L> accounts for more variability in Y
What does R^2 tell us?
the total proportion of variance in Y that is accounted for by the X variables.
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
What is the formula for R^2?
R^2= ryx1^2 +ryx2^2 - 2ryx1ryx2rx1x2/ 1- rx1x2^2
MR uses IV’s to predict what?
DV
What is the MR equation?
y’= b1x1+b2x2+b3x3 + a
y’= DV we are predicting
b= slope
x= raw score
a= intercept
If there is a small difference between the predicted and the actual value this indicates what?
there wasn’t a lot of error
SPSS:(enter method)
L> how do we enter data
separate column for each variable
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)
SPSS(enter method)
L> examining the data results (four boxes)
- box
L> what type of regression was done - 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 - 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. - 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 +/-
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.
SPSS: Forward Method:
L> set up?
- same as the enter method except now you pick forward instead of enter for the model.
SPSS: Forward Method
L> what is the plot made of?
- z-residual on Y and z predicted on x axis!
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!
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.
SPSS: Forward Method
L> F is used to?
- determine if there is a significant addition of that variable!
SPSS: Forward Method
L> Data boxes??
- box
L> only keeps predictors that are significant
( use the largest to interpret because it will include all significant predictors! )
Homoscedasticity?
- error/variance is relatively the same across the regression line!
Linearity?
regression is a straight line!
L> relationship between criterion variable and predictor variable is linear when other predictors are held constant!
