PPA 207: Quantitative Methods
Meeting 7, Spring 2004
1. Homework
Go over calculations on handout
Go over Pollock exercises
Studenmund, chapter 6, number 3
a. I expect that per-capita cigarette consumption (C) and per-capita edible fat
consumption (E) will have a positive effect on death rate. I am uncertain as to the
effect of meat consumption (M), but I expect it will have a non-zero effect.
Therefore I will use one-tailed tests for C and E, and a two-tailed test for M. The
critical value of t at a 10 per-cent level and with 27 dof in a one-tailed test is
1.314, for a two-tailed test it is 1.703. The calculated t statistic for C is 4.0, for E
is 4.0, and for M is 2.0. Therefore I am able to reject the null hypothesis and
"accept" the alternative hypotheses that I have made.
Some may think that M should exert only a positive influence on death rate.
b. If you expect the coefficient on M to be positive, the derived negative
coefficient may be the result of an omitted variable. To determine if a given
variable may possibly be causing the bias, you need to look at expected bias
formula (ß2 * f(rx1,x2)) and see if works out to be a negative bias for any of the
proposed omitted variables.
Liquor should be + related to death rate, and + correlated with meat
consumption: no
Fat content of meat should be + related to death rate, and + correlated with meat
consumption: no
Wine and beer should be + related to death rate, and + correlated with meat
consumption: no
Miles run should be - related to death rate, and - correlated with meat
consumption: no
Open heart surgeries should be - related to death rate, and + correlated with
meat consumption: yes
Oat bran should be - related to death rate, and - correlated with meat
consumption: no
1
c. Given what was just shown in b, I would add open heart surgeries.
Studenmund, chapter 6, number 13
a and b. I would expect Iowa test score and years of parent's education to have a
positive influence on econ test score. I am uncertain about the influence of
nonwhite and female on econ test score but would choose negative if forced.
Thus X3 and X4, which exhibit positive coefficients are likely to be Iowa score or
parent's education. Since X4 exhibits a larger statistical significance (t=12) than
X3 (t=2), and I expect Iowa test score to be more likely to exhibit a positive effect
on econ score, I say X4 is Iowa test score and X3 is parent's education. Thus X1
and X2 are either minority or female. The t-stat on the X1 coefficient is 1.0, on
the X2 coefficient it is 0.25. Since I expect minority to be more likely to exert a
negative influence on test score than female, I would name X1 as minority and
X2 as female.
c. For 19 dofs and a 5 percent confidence level, the critical value of t in a onetailed test is 1.729. In a two-tailed test it is 2.086. The calculated t's on both X1
and X2 is less than both of these critical values so cannot reject the null
hypothesis that gender and race has no influence on econ test score.
d. I did both, but a two-tailed test is preferred because of the uncertain influence
that gender or race has on test scores.
2. Studenmund, Chapter 7, Choosing Functional Form

How are explanatory variables related to dependent?
Curve instead of straight line
Rise to a peak and then fall
Fall to a trough and then rise
All violate standard “linear in the variables” assumption
“Tricks” to deal with

Constant term
Never suppress its use
Figure 7.1 shows problems it creates
Never rely on coefficient for constant term to mean anything

Elasticity
Percentage change in Y for a one-percent change in X

Linear functional form
What we have been using all along
Coefficient represents slope
Elasticity equals coefficient times (mean of Y / mean of relevant X)
Calculated at mean values
2

Log-log functional form
Take log of all variables were possible
Coefficient represents elasticity
Log explanation
e = 2.71828 (natural exponent)
The log of X is the power that e must be raised to equal it
SPSS will calculate it for you
Note that graph of lnY against lnX is linear
Though graph of corresponding Y against X takes on nonlinear
forms in Figure 7.2 depending on value of β

Left log-linear functional form
Take log of only dependent variable
Coefficient represents how Y changes in percentage terms for a one-unit
change in X
Elasticity equals coefficient times mean of X
Note that graph of lnY against X is linear
Though graph of corresponding Y against X takes on nonlinear
forms in Figure 7.3 depending on value of β

Quadratic functional form
Square one of your explanatory variables and add in
Change in Y for a one unit change in X (from a given X value) in quadratic
form is linear coefficient plus (two times quadratic coefficient times chosen
value of X)
Example
Yhat = 3 + 5X – 0.6X2
Slope of this line at X = 2
5 – 1.2 (2) = 2.6
Slope of this line at X =10
5 – 1.2 (10) = -7
See possibilities in Figure 7.4
Solve for inflection point
From previous example
5 – 1.2X = 0
1.2X = 5
X = 5/1.2 = 4.17
Elasticity
[Linear coefficient x (meanX / meanY)] +
[2 x quadratic coefficient x [meanX / meanY)]

See Table 7.1 for summary

Never use adjusted R-squared to pick best functional form
3
Theoretically they cannot be compared because of use of different
dependent variables

Functional form and problems of predicting out of sample
See Figure 7.6
Functional form may not apply outside of sampled data

Standard dummy explanatory variables
Run a regression of Y = yearly salary, X1 = education years, X2 = male
dummy
Figure 7.7: graph result (plug in actual values)

Slope dummy variables
Interaction term
An additional explanatory variable equal to X dummy variable
multiplied by X continuous variable
Why create interaction term?
Figure 7.8: graph result (plug in actual values)
3. Pollock, Chapter 5, Making Controlled Comparisons

Comparison between a Y (dependent) and X variable (explanatory)
holding an alternative causal variable (Z) constant
Either find that Y and X are spuriously related, or an enhanced
relationship after controlling for Z

Open GSS1998.sav
Recreate Polview3
Polviews
1-3 liberal
4 moderate
5-6 conservative
Analyze=>descriptive stats=>crosstabs
Dependent Grass into row
Independent Polview3 into column
Make sure Cells=>columns (%) checked
Crosstab matrix is result
Now add a layer with Kids as control variable

Clustered bar charts
Graphs=>bar=>clustered
Define=>bars represent=>other=>Grass
Change summary=>percentages
High = 1, low = 1
Category axis=>Polview3
Define clusters=>Kids
4
Options=>uncheck display groups by missing values

Multiple-line charts
Better if control variable has lots of categories
Open Nes2000.sav
Analyze=>descriptive stats=>crosstabs
Dependent Gayadopt into row
Independent Educ3 into column
Make sure Cells=>columns (%) checked
Crosstab matrix is result
Now add a layer with Gender as control variable
Graphs=>line=>multiple
Define=>bars represent=>other=>Gayadopt
Change summary=>percentages
High = 1, low = 1
Category axis=>Educ3
Define clusters=>Gender
Options=>uncheck display groups by missing values
4. Homework Due the Start of Meeting Eight
(1) Read all of the material under meeting eight in the syllabus; come prepared to
discuss.
(2) A typed and well developed question from reading assignment for week eight.
(3) Answer question 13 in Studenmund, Chapter 7, typed on a separate page of
paper. Answer questions 1 and 2 in Pollock, Chapter 5, handwritten on given
pages and turn in any requested SPSS output.
(4) Provide a one-paragraph typed and double-spaced write up of the theory that
is behind the regression paper you plan on writing for final project in this course.
Begin with this form:
Dependent variable = f (Broad Causal Factor1, Broad Causal Factor2, Broad
Causal Factor3, Broad Causal Factor4, etc.)
Broad Causal Factor1 = f (actual explanatory variable1, actual explanatory
variable2, etc.)
Broad Causal Factor2 = f (actual explanatory variable3, actual explanatory
variable4, etc.)
Etc.
5
(5) Collect all of the data you will use for dependent variable and enter it into
SPSS. Run Analyze=>descriptive statistics=> frequencies and descriptives.
Turn in computer printout.
(6) Prepare a one-page, single-sided, information sheet that you can bring to
midterm exam next week for use. Turn this in after exam is over.
6