LAB 13 – REGRESSION ANALYSIS #2
MULTIPLE REGRESSION
Purpose
Today’s lab is intended to give you experience working with the basic concepts in multiple regression
analysis (analysis using more than one predictor variable.
Preparation
Computation and Interpretation Assignments
1. From Pagano, Chapter 7, answer question 19. And answer the following two questions.
2. A psychologist studying perceived “quality of life” in a large number of cities (N=200) came up
with the following equation using mean temperature (T), median income in $1,000 (I), per capita
expenditure on social services (S), and population density (D) as predictors. Here are the
unstandardized coefficients:
Yˆ =5.37 – .01(T) + .05(I) +.003(S) – .01(D)
a) Assume that there is a city that has a mean temperature of 55 degrees, a median income
of $12,000, spends $500 per capita on social services, and has a population density of 200
people per block. What is its predicted quality of life score?
b) What would we predict in a different city that was identical in every way except that it
spent $100 per capita on social services.
c) Interpret the intercept
d) Interpret the regression weight for social services
SPSS Assignment - Imagine that you are interested in the association between perfectionism and eating
disorders.
1. Make up an SPSS data set in which you have 80 or more participants, each with a score on a
measure of perfectionism and a score on a measure of eating disorder level. For each variable,
you’ll have to decide the range of scores that the measure could have (eg, the perfectionism
scores might range from 15 to 50…). Make up a data set in which there is a positive association
between the two variables One short cut is to make up a small number of “subjects” (say 15) in
which you have the correlation that you want. Then, copy the data from these 15 subjects and
paste them 5 or 6 times.
2. Use SPSS to compute:
 The correlation between the two variables
 The regression equation in which you predict eating disorders from perfectionism
3. Print the output and:
 Interpret the correlation
 Write out the regression equation in the following format : ED = a + b(P)
 Interpret the intercept and the regression weight
 Interpret the R2 value from the regression output (note that, for one-predictor equations, R2 =
r 2)
Lab Session
Bring your computer to lab
Q& A about lecture
Go over homework assignments
Exercise 1.
A psychologist interested in academic achievement collected data on 100 students. She collected endof-semester GPA’s, and each student also completed a personality inventory measuring the “Big Five”
basic personality traits – Neuroticism (emotional instability), Extraversion (social presence), Openness
to Experience (unconventional thinking), Agreeableness (friendliness), Conscientiousness
(responsibility, impulse control). She conducted multiple regression analyses, with and overall R2
= .121 and the following equations:
Unstandardized coefficients:
GPA = 2.02 - .00127(N) + .00139(E) +.00859(O) - .00279(A) + .02155(C)
Standardized coefficients:
GPA = -.046(N) + .058(E) + .142(O) - .111(A) + .332(C)
a) Interpret the overall R2
b) Which trait is the best predictor of GPA – explain how you know. Psychologically speaking ,
what does this tell us about the association between personality and academic achievement?
c) Imagine that she then added IQ as a sixth predictor in the equation and the R2 of the new model
is .20. What do these results tell us about the association between IQ and GPA.
Exercise 2.
During the previous lab section, you ran a series of one-predictor analyses, examining some family predictors of
Child IQ. Today, we’ll run a multiple regression analysis to answer some more complex questions.
Use the SPSS file from last time (ChildIQ.sav) – either find it on your hard drive, or download it from the class
web site. Recall that this data file includes real data from 200 families. For each family, there are several
variables – Child IQ, Father’s daily salary (in dollars), a dichotomous variable representing Parents’ marital
status (0=married, 1=divorced), and Mothers’ IQ.
1. Compute and interpret the correlations among the 4 variables. Pay particular attention to these “zero-order”
correlations between Child IQ and the other three variables.
2.. Run a regression analysis using Father’s daily salary and Mother’s IQ as predictors of Child IQ.
 Analyze  Regression  Linear
 Put Child IQ in the Dependent variable box and put Father’s daily salary and Mother’s IQ in the
Independent variables box
 Push the OK button
3. Interpret the regression equation
 R2
 Significance test of R2
 What would it mean if the sig test of R2 was non-significant? What would such a result tell us about
these two predictors of Child IQ?
 Intercept
 Unstandardized regression weight for Father’s daily salary
 Significance test of Father’s daily salary
 Unstandardized regression weight for Mother’s IQ.
 Significance test of Mother’s IQ
 Which is the stronger predictor, in terms of effect size?
 Compare the Betas to the zero-order correlations from #1, above. Note that the correlation between
child IQ and Father’s Salary was moderately small, but statistically significant; however, the Beta for
Father’s salary is very small and non-significant. Why the difference? What might this imply about the
factors affecting Child IQ?
4. Add the “Marital Status” variable as a third predictor of Child IQ.
 Interpret the results of the analysis – refer back to the “zero-order” correlations to help interpret what
might be going on.
Imagine that we had discovered that “Marital Status” had a large and statistically significant negative
standardized regression weight. Based on that, I might be tempted to conclude that, if we convinced parents to
remain married, then we could help maintain higher levels of Child IQ. Could this be true? How? Why should I
not draw this conclusion (again, even if the effect of Marital Status was large and statistically significant)?