1. Zac Bodner, Lab Assignment #3
Introduction
Students in Dr. Davis’ undergraduate Marketing Analytics class took a survey on campus to find
out about what students thought of certain prominent political figures. The following is an
exploration of some of the findings of the survey, and their implications.
Correlation Matrix
Using SPSS, I entered all of the variables included in the survey into a correlation matrix. The
purpose of this activity is to examine R values, which represent the strength of the correlation
between two variables.
I found significant, positive relationships between the variable (Masculinity) and the variables
Ted Cruz like you, and Ted Cruz intelligent. I found these same relationships between
Masculinity and Donald Trump like you, and Donald Trump intelligent. Conversely, I found a
significant, inverse relationship between Masculinity and other Hillary Clinton variables,
particularly - like you.
This suggests that conservative ideologies (based more on feeling and belief than fact) are
considered masculine, and liberal ideologies (based on fact and intellectual exchange of ideas)
are considered feminine. This also suggests something fairly obvious to most humans, that
“birds of a feather flock together.”
Regression Analysis
Next, I set out to investigate this further. I ran a single outcome regression with the dependent
variable - Ted Cruz I Have A Good Impression of him, and the independent variable - Masculine.
I found that there was a positive relationship between these two variables. That is to say, the
more masculine someone considers themselves, the more likely they are to have a positive
impression of Ted Cruz. However, the standardized beta weight of the association (the same as
R in this case, since there is only one variable to compare) was not very strong at .032. The p-
value of this association was not particularly significant either - coming in at .238 (meaning, this
association is due to chance 28% of the time).
Adding more variables (feminine, your ideology, grew up, travel) to the regression changed the
significance, and the weights of their cumulative effect on the dependent variable. For example,
the beta weight of “masculine” jumped from .032 to .104, and it’s significance increased to .026.
“Travel” and “grew up” had high significance rates, so I dropped them from the model and
created a new one. This one only contained the variables masculine, feminine, and your
ideology.
Doing this yielded a model that produced an R square of .139. This means that the combination
of these three independent variables explains about 14% of the variance in the dependent
variable - Ted Cruz I Have A Good Impression of Him. Or, they explain about 14% of the
reasons why people have varying impressions of Ted Cruz. The p values are all below .05, so
95% of the time these variables are not associated by chance. The strongest association was
2. between “your ideology” (-.358) and the dependent variable. This weight suggests that the less
liberal a respondent was, the more likely they were to have a favorable impression of Ted Cruz.
The question at this point is why do these variables lose or gain power when combined with
other variables? The reason for this is that the independent variables are not only related to the
dependent variable, but also to each other.
Let’s visual an example. Our dependent variable is how much we like Ice Cream. If we ran a
regression with one independent variable - sweetness - the strength of that association would
be very high. If we threw in another variable - creaminess - then sweetness would now only be
part of the reason we like ice cream, and it’s particular effect would be diluted, because it is now
combined with another reason we like ice cream - because it is creamy.
The more independent variables we must account for, the more their strengths will tie into each
other. With Ted Cruz’ impression, the strength of the effect of “masculinity” will be mitigated
when combined with another variable, like “your ideology.” This happens for the same reason as
the ice cream example. We don’t just like ice cream because it’s sweet, now we like it because
it’s creamy, too. So the variables have to share space, like in a pie chart of ice cream affection.
So with Ted, we don’t just have a high impression of him because we are masculine and think
he is too. Now. we have a high impression of him because we are masculine, and because he
shares a political ideology with us. So these two variables both explain parts of the reason for
our impression of him, but do to the fact that there are more factors to account for - their
individual strength wanes.
