lecture 4- multiple regression

Question 1

describing correlation:

Answer 1

Correlation: relationship between 2 variables
* calculate r and R2

Question 2

predicting simple linear regression:

Answer 2

Simple linear regression: predicting one variable from another variable
* calculate R and R2

Question 3

describing partial correlation:

Answer 3

Partial correlation: relationship between 2
variables while accounting for another variable
or variables
* calculate partial r and R2

Question 4

predicting multiple linear regression:

Answer 4

Multiple linear regression: predicting one variable
from 2+ other variables
* calculate multiple R and multiple R2

Question 5

least squares- regressions

Answer 5

simple linear regression equuation: Y= a + bX + error

Question 6

variance accounted for (R2)- regressions

Answer 6

How well does variable X predict variable Y?
How much variance in Y can be predicted from X?

Question 7

equation for simple and multiple linear regression

Answer 7

simple: Y^ = a + b1x1
multiple: Y^ = a + b1x1 + b2x2 + b3x3 + K bk xk

Question 8

simple linear regression

Answer 8

R is the correlation between the criterion variable and a single predictor (ignoring all other possible predictors).
R2 (coefficient of determination) is the amount of variance explained by that single predictor.

Question 9

multiple regression:

Answer 9

Multiple R is the correlation between a criterion variable and multiple, weighed predictors (i.e., the effect of each
predictor after controlling for the effects of the other predictors).
Multiple R2 (coefficient of multiple determination) is the amount of variance explained by those multiple predictors.

Question 10

simple and multiple linear regression

Answer 10

The multiple regression equation is an extension of the bivariate equation.
* the constant (a) which represents value of Y when all predictor variables (x1, x2, x3…) are zero.
* There is a b weight for each of the predictors (x1, x2, x3…).
→ These are partial regression coefficients.
→ These weights represents the change in Y associated with a 1-unit change in a particular X,
when all other Xs are held constant

Question 11

Y with an accent on top = there will be error in prediction

Question 12

error=

Answer 12

varience in the model that is not explained

Question 13

least squares:

Answer 13

find regression line that provides the best prediction possible ie a regression line that minimises error

Question 14

regressions=

Answer 14

how much of the varience in a data set is accounted for by the predictor (s)

Question 15

what are the three types of multiple regression analyses?

Answer 15

Simultaneous (direct entry) regression:
* all the variables are entered in together, irrespective of their absolute or relative importance
Hierarchical regression: you decide (you can enter variables in blocks, with your decisions being driven by
previous research and hypotheses).
Stepwise (statistical) regression:
* Forward regression: your computer programme (e.g., SPSS) will find the single best predictor and enter it as
the first variable; the variable that accounts for the highest proportion of the remaining variance is entered
next and so on
* Backward regression: all variables are entered initially and the worst predictors (i.e., the predictors that
account for the least variance) are removed in turn