Sociology and Regression Analysis Practice Flashcards

Forty vocabulary terms and definitions based on lecture notes covering regression analysis, causal criteria, and dummy variables.

Partial coefficients

Indicators used to express that there is a partial impact within a regression model.

R-squared of $.60$

Means that $60\%$ of variance in $Y$ is explained by $X$.

Beta coefficient interpretation

Represented as a change in standard deviations units; for every $1$ standard deviation change in the predictor, there is a specific change in the outcome.

Big gap between $R^2$ and Adjusted $R^2$

An indicator of a poor model.

Small gap between $R^2$ and Adjusted $R^2$

An indicator of a strong model.

Spurious relationship

A relationship where variables are not causally related to each other, but it may be wrongly inferred that they are.

Reference group

The group to which other categories are being compared when using a dummy variable.

P-value

A value that tells us the significance of a variable.

Control factor for Spurious relationships

A relationship that disappears after controlling for a $3rd$ variable.

Partial slope

Differs from a bivariate slope because it controls for other predictors in the model.

Causal claim caution (Social Media)

The conclusion that evidence is consistent with the claim that social media use causes depression, but alternative explanations can still exist.

$k-1$ rule

The formula used to determine the number of dummy variables; for example, if race has $3$ categories (white, black, and other), you need $2$ dummy variables.

$$p = .02$$

A p-value that is significant, meaning we should reject the null hypothesis.

Dummy variable comparison

Variables that compare a group only to the reference group, rather than to all groups.

Interaction (Wealth example)

Occurs when Education predicts income among low-wealth individuals but not among high-wealth individuals.

$Educ = -.110$ (Children analysis)

Means that for each additional year of education, there are $.110$ fewer children, controlling for siblings.

Adjusted $R^2$ vs. $R^2$

The Adjusted R-squared differs because it penalizes for the addition of variables to the model.

Relative Strength of Coefficients

Determined by highest absolute value; in the transcript example, Sibs ($.127$) is considered stronger than Educ ($-.191$).

Phi coefficient near $.01$

Suggests little or no association within a $2 \times 2$ table because the value is close to $0$.

Interaction (Pattern definition)

A pattern where the $X-Y$ association differs across the levels of $Z$.

Improved Model Fit

Indicated by an increase in Adjusted $R^2$, such as from $.009$ to $.294$ when adding education to the model.

Stata regression syntax

The requirement that the dependent variable is placed first, before the independent variables.

Time order

A causal criterion stating that the cause must occur before the outcome.

Chain/mediating relationship

A relationship where $X$ affects $M$, and $M$ affects $Y$.

Intercept (Alpha)

The Y-intercept, representing the predicted value of $y$ when all independent variable values are $0$.

Standardized beta coefficient

A coefficient that is useful for comparing predictors that were measured in different metrics.

Observational research limitation

The fact that it can rarely prove causality definitively because there are almost always alternative explanations.

$R^2$ (Bivariate context)

Tells us how much $X$ and $Y$ relate, or the variance in $y$ explained by $x$..

Odds Ratio calculation

Calculated as $6$ based on: trained survived ($42$), trained died ($14$); untrained survived ($24$), untrained died ($48$).

Equal group sizes

A factor that is not a causal criterion, despite common misconceptions.

Association

The first criterion for causality: as $X$ changes, so does $Y$.

Eliminating alternative explanations

The third criterion for causality, involving the removal of all other reasonable expectations.

Black Student interpretation (Reference White)

If white is the reference and the black coefficient is $-1.23$, black students are $-1.23$ lower at a starting point when white is $0$.

Complete explanation

Term used when a zero-order relationship disappears after controlling for a variable like friend group.

Shrinking coefficient (Race/Education)

When the black coefficient shrinks after adding education, it means education explains some of the racial difference in occupational prestige.

Predicted value at Intercept $46.49$

Calculated as $45.26$ for a black student when the black coefficient is $-1.23$.

Causality Criterion: Time Order definition

Something that happens before what we are predicting.

Model fit and coefficient reduction

The interpretation when adding education reduces the race coefficient: education explains part of the original race difference.

Metric comparison utility

The primary reason the standardized beta coefficient is utilized.

Inferred causal relationship

A characteristic of spurious correlations where variables are wrongly thought to be causally related.