PSY 555 Homework 16

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 b3 and b4.  Since values of 0.00 cannot reasonably occur for all predictors, the intercept has no meaningful interpretation.

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=.60516X1-.33399X2+4.5882X3+.07023X4+1.66926.

5.4(b).   β1=.624

β2=-.311

β3=.514

β4=.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.