[L11] Multiple Regression Analysis

Question 1

__ (rather correlation) is the term used when we have
the specific aim of predicting values on a ___ variable (or
target) from a “
__ variable”.

Answer 1

Regression; criterion; predictor

Question 2

The square of ___gives us an estimate of
the variance in y explained by variance in x.

Answer 2

correlation coefficient

Question 3

Because there is a correlation between x and y , we can to a
certain extent, dependent on the size of r², predict __
from x scores.

Answer 3

y scores

Question 4

line of best fit placed among the
points in a scatterplot.

Answer 4

REGRESSION LINE

Question 5

REGRESSION LINE

On this line will lie all our
___,
symbolized as ŷ, made from our knowledge of x values.

Answer 5

predicted values for y

Question 5

The vertical line between an actual y value & its
associated ŷ value is known as

Answer 5

PREDICTION ERROR.

Question 6

But it is better known as a ____ because it
represents how wrong we are in making the prediction for
that particular case.

Answer 6

RESIDUAL

Question 7

The
_
__ then is a line that minimizes these
residuals

Answer 7

regression line

Question 8

__– it is the number of units Ŷ increases
for every unit increase in x.

Answer 8

Regression coefficient

Question 9

_ is a constant value. It is the value of Ŷ when x is 0

Answer 9

c =

Question 10

In regression we also deal with___ rather than raw
scores

Answer 10

standard scores

Question 10

When scores (x and y) are expressed in standard score form
then the regression coefficient is known as the
__

Answer 10

STANDARDIZED REGRESSION COEFFICIENT or
BETA

Question 10

Where there is only one predictor, __ is in fact the correlation
coefficient of x with y.

Answer 10

beta

Question 10

_
* Can be used when we have a set of variables (x1, x2, x3 etc)
each of which correlates to some extent with a criterion
variable (y) for which we would like to predict values.

Answer 10

MULTIPLE PREDICTIONS

Question 10

_ of two variables (green portion is the
shared variance) = r²

Answer 10

Co-variation

Question 11

Because multiple regression has so much to do with
correlation, it is important that the variables used are
__.

Answer 11

continuous

Question 12

That is, they need to incorporate measures on some kind of a
___ scale

Answer 12

linear

Question 13

In __, variables like marital status where codes 1-4 are
given for single, ,married, divorced, widowed etc. can not be
done

Answer 13

correlation

Question 14

The exception, as with correlation, is the __ variable
which is exhaustive, such as gender.

Answer 14

dichotomous

Question 15

Even with these variables, however, it does not make sense to
carry out a __ regression analysis if almost all variables
are dichotomously categorical

Answer 15

multiple

Question 16

if almost all variables
are dichotomously categorical, In this instance a better procedure would be __

Answer 16

LOGISTIC
REGRESSION

Question 17

__
* Refers to predictor variables that will also correlate
with one another

Answer 17

COLLINEARITY

Question 18

If one IV is to be a useful predictor of the DV, independently
of its relationship with another IV (collinearity), we need to
know its unique relationship with the dependent variable.
* This is found using the statistic known as the ___

Answer 18

SEMI-PARTIAL
CORRELATION COEFFICIENT

Question 19

___is a way of partialling out the
effect of a third variable (z) on the correlation between two
variables, x and y.

Answer 19

PARTIAL CORRELATION

Question 20

In __ correlation we take the residuals of only one of the two variables involved.

Answer 20

semi-partial

Question 21

Semi-partial correlation gives us the ___ only shared between an IV & the DV, with the variance of another IV partialled out.

Answer 21

common variance

Question 22

Remember that the explained variance is found by ___

Answer 22

squaring the regression coefficient.

Question 23

Now, imagine that for each predictor variable a regression coefficient is found that, when squared, gives us the unique variance in the DV explained by that predictor on its own with the effect of all other predictors partialled out In this way we can improve our prediction of the variance in a dependent variable by adding in __ in addition to any variance already explained by other predictors

Answer 23

predictors that explain variance in y

Question 24

In multiple regression, then, a ___ of one variable is made using the correlations of other known variables with it.

Answer 24

statistical prediction

Question 25

For the set of predictor variables used, a particular combination of __is found that maximizes the amount of variance in y that can be accounted for.

Answer 25

regression coefficients

Question 26

In multiple regression, then, there is an ___ that predicts y, not just from a x as in single predictor regression, but from the regression coefficients of X1, X2, X3 and so on.. Where Xs are predictor variables whose correlations with y are known.

Answer 26

equation

Question 27

bi are the __

Answer 27

regression coefficients for each of the predictors (xi)

Question 28

bo is the __ (c in the simple example earlier)

Answer 28

constant

Question 29

These b values are again the ___increases for each unit increase in the predictor (xi), if all the other predictors are held constant.

Answer 29

number of units Ŷ

Question 30

However, in this multiple predictor model, when standardized values are used, the ___are not the same value as that predictor’s correlation with y on its own.

Answer 30

standardized regression coefficients

Question 31

What is especially important to understand is that, although a single predictor variable might have a strong individual correlation with the criterion variable, acting among a set of predictors it might have a __

Answer 31

very low regression coefficient.

Question 32

In this case the potential contribution of one predictor variable to explaining variance in DV has, as it were, already been mostly used up by another predictor or IV with which I shares a lot of __

Answer 32

common variance

Question 33

The multiple regression procedure produces a __, symbolized by R, which is the overall correlation of the predictors with the criterion variable. * In fact, it is the simple correlation between actual y values & their estimated y values.

Answer 33

MULTIPLE CORRELATION COEFFICIENT

Question 34

The higher R is, the _ _ between actual y value & estimated ŷ.

Answer 34

better is the fit

Question 35

The closer R approaches to +1, the ___ the differences between actual & estimated value

Answer 35

smaller are the residuals –

Question 36

Although R behaves just like any other correlation coefficient, we are mostly interested in R² since this gives us the __ in the criterion variable that has been accounted for by the predictors taken together.

Answer 36

proportion of variance

Question 37

This is overall what we set out to do – to find the ___ to account for variance in the criterion variable.

Answer 37

best combination of predictors

Question 38

To find an R that is significant is __

Answer 38

no big deal

Question 39

This is the same point about __ correlations, that their strength is usually of greater importance than their significance, which can be misleading.

Answer 39

single

Question 40

However, to check for significance the R² Value can be converted into an __

Answer 40

F value

Question 41

R² has to be adjusted because with small N its value is artificially __.

Answer 41

high

Question 42

This is because, at the extreme, with N = number of predictor variables (p) + 1, prediction of the criterion variable values is __ and R² = 1, even though, in the population, prediction can not be that perfect.

Answer 42

perfect

Question 43

The issue boils down to one of __

Answer 43

sampling adequacy.

Question 44

Various rules of thumb are given for the __to produce a meaningful estimate of the relationship between predictors & criterion in the population – remember we are still estimating population parameters from samples.

Answer 44

minimum number of cases (N)

Question 45

Although some authors recommend very high N indeed, Some recommend that the minimum should be __, and most accept this as reasonable, though the more general rule is __

Answer 45

p + 50; “as many as possible”.

Question 46

Effect Size

Answer 46

Small = .02 * Medium = .15 * Large = .35

Question 47

The output table in Multiple Regression Analysis\

Answer 47

* 1st table - simple descriptives for each variable. * 2nd table - correlation between all variables. * 3rd - which variables have been entered into the equation

Question 48

* Model Summary –

Answer 48

gives R, R², and adjusted R²

Question 49

Tells whether or not the model accounts for a significant proportion of the variance in the criterion variable. It is a comparison of the variance “explained” vs. the variance “unexplained” (the residuals)

Answer 49

* ANOVA –

Question 50

- – contains information about all the individual predictors

Answer 50

Coefficients

Question 51

__ – are the b weights. This tells us how many unit/point increase will there be in the criterion variable for every 1 unit/point increase in a particular predictor variable.

Answer 51

Unstandardized Coefficients

Question 52

__- are the beta values. This tells us how many SD unit increase will there be in the criterion variable for every 1 SD unit increase in a particular predictor variable.

Answer 52

Standardized Coefficients

Question 53

__– found by dividing the unstandardized b value by its standard error. If t is significant, it means the predictor is making a significant contribution to the prediction of the criterion.

Answer 53

t-values

Question 54

__ – when predictor variables correlate together too closely. If tolerance values in the coefficients table are very low (e.g., under .2) then multicollinearity is present.

Answer 54

Collinearity