Marketing Analytics & OLS Regression Flashcards

Vocabulary practice flashcards covering R data manipulation, Ordinary Least Squares (OLS) regression, hypothesis testing, and statistical error types based on lecture notes.

Ordinary Least Squares (OLS) Regression

A statistical technique for modeling the relationship between an outcome variable ($Y$) and one or more predictor variables ($X$) by minimizing the sum of squared residuals.

Residual ($e$)

The difference between an actual observed outcome value (Y_i) and the predicted value (X_i) generated by a regression model.

R-squared ($R^2$)

The percentage reduction in prediction error achieved when using a fitted regression model compared to using an uninformed baseline mean guess.

Continuous Variable

A quantitative variable that can take on any numerical value within a given continuous range.

Categorical Variable

A qualitative variable that represents discrete, non-smooth buckets or specific categories rather than continuous numeric values.

Reference Level

The baseline category in a categorical regression model whose mean is represented by the intercept ($\beta_0$), against which other categories are compared.

Null Hypothesis ($H_0$)

An assumed state of the world (typically representing no effect, no relationship, or "no") that is held as true until sample evidence sufficiently contradicts it.

Alternative Hypothesis ($H_a$)

The hypothesis that contradicts the null hypothesis, representing the state of the world (such as an effect or difference) that an experiment aims to support.

p-value

The probability of observing a sample statistic at least as extreme as the one obtained, assuming that the null hypothesis ($H_0$) is true.

Significance Level (alpha)

The probability threshold (conventionally set at $0.05$) used to decide whether to reject or fail to reject the null hypothesis.

Type I Error

A "false positive" error that occurs when a researcher rejects a true null hypothesis ($H_0$).

Type II Error

A "false negative" error that occurs when a researcher fails to reject a false null hypothesis ($H_0$).

Multiple Testing Problem

The inflation of the cumulative probability of committing at least one Type I error when performing multiple simultaneous hypothesis tests.

Categorical Predictor Regression (Visual Model)

A visual representation of the regression model $\text{Profit} = \beta_0 + \beta_1 \times \text{Category} + e$, where $\beta_0$ is the mean of the reference group (Category 1) and $\beta_1$ is the difference in means between Category 2 and Category 1.

p-value Factors (Visual Comparison)

A comparative distribution diagram demonstrating that the p-value accounts for both the size of the "effect" (distance between distribution means) and the variability in the data (distribution width).

Type I and Type II Errors (Visual Distribution)

A diagram displaying hypothesis testing errors where Type I error corresponds to rejecting $H_0$ when $H_0$ is true ("False Positive") and Type II error corresponds to failing to reject $H_0$ when $H_0$ is false ("False Negative").

False Positive Probability Curve (Multiple Testing)

A plot demonstrating how the cumulative probability of at least one false positive ($1 - 0.95^k$) increases dramatically as the number of independent hypothesis tests ($k$) grows.