PSY 555 Homework 16

Answers

Chapter 15: #1,2,3,4

15.1(a). Predicting Quality of Life:

All
other variables held constant, a difference of +1 degree in Temperature is
associated with a difference of -01 in perceived Quality of Life. A difference of $1000 in median Income, again
all other variables held constant, is associated with a +.05 difference in
perceived Quality of Life. A similar
interpretation applies to *b _{3} *and

15.1(b). Y=5.37-.01(55)+.05(12)+.003(500)-.01(200)=4.92

15.1(c). Y=5.37-.01(55)+.05(12)+.003(100)-.01(200)=3.72.

15.2.
A
difference of +1 standard deviation in Temperatuer is associated with a
difference of -.438 standard deviations in perceived Quality of Life, while a
difference of +1 standard deviation in Income is associated with about three
quarters of a standard deviation difference in perceived Quality of Life. A similar interpretation can be made for the
other variables, but in all cases it is assumed that all variables are held
constant except for the one in question.

15.3. _{}

I
would thus delete Temperature from the model, since it has the smallest t, and
therefore the smallest semi-partial correlation with the criterion variable.

5.4(a). Predicting job satisfaction:

Y=.60516X_{1}-.33399X_{2}+4.5882X_{3}+.07023X_{4}+1.66926.

5.4(b). β_{1}=.624

β_{2}=-.311

β_{3}=.514

β_{4}=.063

1. Variables
that are collinear are variables that are highly correlated with each
other. Collinear variables, if both used
in a regression model, may account for the same portion of a criterion
variable’s variance. So, when you use
two collinear variables in a regression model, one may not provide any
additional explanation of variance to the model and so one may not be useful.

2. While
there is no exact method for how to choose the order with which you enter variables
into your regression equation. If you
have a theory about the factors that are likely to be good predictors of a
criterion, then you would enter the variables into the equation in the order
that theory supports (e.g., the variable expected to be the best predictor
first, then the next most influential variable, etc.). Otherwise, you would need to determine the
order of variables by performing exploratory analyses. You would look at all plots of the variables
against one another and determine which variable explains the most variation in
the criterion variable. Then you could
run regression with that variable as a predictor and, after examining the
residuals plotted against the remaining predictors, determine which variable
next accounts most for the variation, in the criterion variable, that is not
explained by the first variable in the model.
Then you would take the next best variable and enter it second into the
regression model. You would repeat the
process until there were no more useful predictor variables left. To confirm that the model (and variable
order) is appropriate, we can then run confirmatory analyses testing the model
we selected from the exploratory analyses.