Stat 102 Final Exam

Front 1

Threats to causal relationships

Back 1

Reverse causation, confounding variables

Front 2

Confounding variables

Back 2

Additional factors that might lead us to give too much “credit” to an explanatory variable.

Front 3

What does the coefficient of X1 mean? (multivariate regression with X1 and X2 as variables)

Back 3

This is the relationship between X1 and Y
- controlling for X2
- holding X2 constant
- controlling for the linear relationship between X2 and Y

Front 4

What does the coefficient of the constant mean? (multivariate regression with X1 and X2 as variables)

Back 4

This is the expected value for when both X1 AND X2 are 0.

Front 5

R-squared

Back 5

Measure of the proportion of the variance in the dependent variable explained by the independent variables

Front 6

Calculate R-squared

Back 6

(Variance of Y - Sum of Squared Residuals)/Variance of Y

Front 7

When would you use an F-test?

Back 7

- Nominal variables
- Variables likely to be highly correlated, but important predictors

Front 8

Unrestricted model

Back 8

Includes independent variables you want to test joint significance of

Front 9

Restricted model

Back 9

Same model, excluding independent variables to be best tested

Front 10

Interpret the coefficient on X1 (multivariate regression).

Back 10

The coefficient on X1 indicates that - controlling for other variables in the model - _ (e.g. for every additional unit, Y changes by _...). Because the p-value is less than .05 we can be 95% confident that this relationship is different from zero (if significant).

Front 11

Dichotomous dependent variable.

Back 11

Probability or percentage, use PERCENTAGE POINTS when interpreting the coefficient

Front 12

Why would the coefficient on X1 drop when you add X2 and X3 to the model?

Back 12

X2 and X3 are related to X1 as well as Y. Failing to account for X2 and X3 would result in overestimating the effects of X1. Without adding X2 and X3, the relationship between X1 and Y is confounded by other factors that might affect Y.

Front 13

When do you log an independent variable?

Back 13

When the data is skewed

Front 14

How do you confirm that a variable contributes to the predictive power of the model when you are using that variable AND its squared term?

Back 14

Use an F-test to check for joint significance.

Front 15

F test

Back 15

A way to test whether adding a set of variables reduces the sum of squared residuals enough to justify throwing these new variables into the model.

Front 16

What does the F test depend on?

Back 16

- How much the SSR is reduced
- How many variables you are adding
- How many cases you have to work with

Front 17

Why would you use nominal rather than ordered variables (e.g. party identification).

Back 17

The change from one value to another might not be the same, e.g. from -3 to -2 and 0 to 1.

Front 18

What does the coefficient on X1-squared tell us?

Back 18

Including X1-squared and allowing for a curved relationship between X1 and Y improves the fit of the model (if significant).

Front 19

Interpret the coefficient on X1*X2.

Back 19

For every one unit increase in X1, the slope of the relationship between X2 and Y will (increase/decrease) by (coefficient).
AND for every one unit increase in X2, the slope on the relationship between X1 and Y will (increase/decrease) by (coefficient).

Front 20

What does it mean when the coefficient of X1*X2 is statistically significant?

Back 20

This means that the slope of the relationship between X1 and Y is significantly different depending on the value of X2 (and vice versa).

Front 21

Interpreting a graph of relationships involving an interaction term

Back 21

- Is the slope greater for one group than the other (is the relationship stronger)
- Where is the difference between the two groups greatest?

Front 22

Interpret the coefficient on X1 (multivariate regression including an interaction term)

Back 22

The slope of the relationship between X1 and Y = _ when X2 = 0 (and vice versa).

Front 23

What does random assignment guarantee?

Back 23

Treatment and control groups will be similar except for the fact that one group is “treated” - any change will be due to treatment

Front 24

External validity

Back 24

Would what you find actually happen outside of the context of an experiment?

Front 25

Field experiment

Back 25

Intervention done while people are going about their business. PRO: external validity
CON: no experimental control, ethical issues

Front 26

Pros/cons of observational analysis

Back 26

PRO
- Can “find” data – don’t have to gather it yourself
- Sometimes the only reasonable approach (e.g. what causes war?)
CON
- Difficult to definitively determine causation
BUT if our model is good we can get good estimates

Front 27

Pros/cons of experiments

Back 27

PRO
- Identifying causality
- Eliminates confounding variables
- Random assignment, experimental control
- Detail - e.g. break down process into smaller units
- Precise measurement

CON
- External validity (can results be replicated outside of the context of an experiment?
- Unrepresentative subject pools (college students)
- Experimenter bias (e.g. demand characteristics, expectancy effects)

Front 28

Experiment null and alternative hypotheses

Back 28

H0: no difference between the treatment groups
HA: difference between the treatment groups

Front 29

Test for difference in proportions

Back 29

Difference of proportions/Standard error of this difference

Front 30

CLT in relation to difference in proportions

Back 30

In repeated sampling, the distribution of our estimates of the mean (or difference of means or slope) will be normally distributed and centered over the true population value

Front 31

Why might the standard error of a regression coefficient be small?

Back 31

Large N

Front 32

Find the T-value of a regression coefficient.

Back 32

Coefficient/Standard Error

Front 33

How would adding X2 affect the coefficient of X1? Why/why not and how?

Back 33

Depends on whether X2 is associated with X1. If it is, then adding X2 would probably reduce the coefficient on X1. Including X2 as a control is a way to avoid giving X1 explanatory "credit" for variation in Y that can also be explained by X2.

Front 34

Is X1 a statistically significant predictor of Y? How do you know?

Back 34

If the p-value is less than .05, then X1 is a statistically significant predictor of Y.

Front 35

What does the coefficient on _ mean?

Back 35

This is the estimate of the relationship between X1 and Y.
USE "predicted" "expect" "estimated"
e.g. For every additional unit of X1, we expect Y to increase by _.

Front 36

Is the relationship between X1 and Y causal?

Back 36

Use theory, but if not, this is likely due to X1 being associated with other factors that cause Y.

Front 37

Suppression

Back 37

Omitting a variable from the regression model CAN suppress the estimate of an independent relationship

Front 38

How do we know that there is actually a difference in proportions?

Back 38

If 0 was the true difference, it would be very unlikely that we would find a difference (T-value) standard errors from 0 be chance

Front 39

Demand Effect

Back 39

Performing an experiment creates results e.g. a researcher unconsciously changing their behavior to get the result they want - considered a confounding variable