BUAL 2650 Exam 2: Analytics for Business Decisions Vocabulary

Comprehensive practice flashcards covering vocabulary, statistical definitions, key formulas, and diagnostic chart interpretations for BUAL 2650 Exam 2.

Qualitative Data

Non-numerical categories or labels (such as gender, state, satisfaction level, or payment method) used to classify items, displayed graphically using bar charts and pie charts.

Quantitative Data

Numeric, measurable values with meaningful units (such as age, revenue, temperature, or height) displayed using histograms, scatter plots, and line graphs.

Discrete Random Variable

A numerical variable whose values are counted in distinct whole steps ($0, 1, 2, \text{etc.}$), such as the number of customers per hour or defective items.

Continuous Random Variable

A numerical variable that can take on any real value along an unbroken scale or continuum (such as waiting time, coffee temperature, or revenue), required for the normal distribution.

Empirical Rule

A guideline for normal distributions stating that approximately $68.27\%$ of data falls within $\mu \pm 1\sigma$, approximately $95.45\%$ falls within $\mu \pm 2\sigma$, and approximately $99.73\%$ falls within $\mu \pm 3\sigma$.

$z$-Score

A standardized measure calculated as $z = \frac{x - \mu}{\sigma}$ that indicates how many standard deviations an observation ($x$) lies above or below the population mean ($\mu$).

Inferential Statistics

The branch of statistics that uses sample data to draw conclusions, estimate parameters, and make decisions about an entire population.

Confidence Interval (CI)

A range of plausible values derived from sample data that is likely to contain the true, unknown population parameter, structured as $\text{Point Estimate} \pm \text{Margin of Error}$.

Margin of Error (ME)

The maximum expected difference between the true population parameter and a sample point estimate at a specified confidence level, calculated as the critical value multiplied by the standard error.

Confidence Level

The long-run percentage or probability, denoted as $(1 - \alpha) \times 100\%$, that repeated independent samples will produce confidence intervals containing the true population parameter.

Hypothesis Testing

A statistical procedure that uses sample evidence to evaluate the validity of a specific claim or assertion regarding a population parameter.

Null Hypothesis ($H_0$)

The starting baseline assumption representing the status quo, no effect, or claimed benchmark value, which always contains the equality sign ($=$).

Alternative Hypothesis ($H_1$ or $H_a$)

The competing claim or hypothesis that represents a change, difference, or effect, expressed using directional or non-directional inequalities ($<, >, \text{ or } \neq$).

Significance Level ($\alpha$)

The predetermined threshold representing the maximum acceptable probability of committing a Type I error (commonly set at $0.05$ or $0.01$).

$p$-Value

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

Type I Error

The error made when rejecting a null hypothesis ($H_0$) that is actually true (a false positive), occurring with probability equal to $\alpha$.

Type II Error

The error made when failing to reject a null hypothesis ($H_0$) that is actually false (a false negative), failing to detect a real effect.

A/B Testing

A randomized experimental technique used to compare two versions—a control ($A$) and a treatment ($B$)—to evaluate which yields superior performance in key business metrics.

Control Group (Version A)

The existing or standard version of a webpage, app, or business process that serves as the baseline for comparison in an A/B test.

Treatment Group (Version B)

The modified, newly proposed version in an A/B experiment tested to determine if it produces a statistically significant improvement over the control.

Paired Test Design

An experimental setup where the exact same subjects or units are measured under both conditions (control and treatment), evaluated with degrees of freedom $df = n - 1$ where $n$ is the number of pairs.

Dependent Variable ($Y$)

The response or outcome variable that a researcher seeks to predict, quantify, or explain using regression modeling.

Independent Variable ($X$)

The explanatory or predictor variable used in regression analysis to explain variation in or make predictions about the dependent variable ($Y$).

Scatter Plot Linearity Assessment

An initial graphical evaluation of paired $(X, Y)$ data on a Cartesian plane to verify whether points follow a straight-line trend (linear), curved pattern (nonlinear), or show no relationship.

Simple Linear Regression Population Model

The theoretical relationship expressed as $Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i$, composed of a deterministic linear component ($\beta_0 + \beta_1 X_i$) and a random error component ($\varepsilon_i$).

Least Squares Method

The estimation procedure that determines the best-fitting line by minimizing the sum of the squared vertical differences between observed and predicted values ($\text{SSE} = \sum (y_i - \hat{y}_i)^2$).

Residual ($e$)

The difference between the observed value and the predicted value of the dependent variable for a given observation, calculated as $e = y - \hat{y}$.

Correlation Coefficient ($r$)

A standardized metric measuring the strength and direction of a linear relationship between two quantitative variables, bounded such that $-1 \le r \le 1$.

Coefficient of Determination ($R^2$)

The proportion of total variation in the dependent variable ($Y$) explained by variation in the independent variable ($X$), computed as $R^2 = \frac{\text{SSR}}{\text{SST}}$ and bounded such that $0 \le R^2 \le 1$.

Mean Square Error ($MSE$)

The point estimate of the residual variance ($\sigma^2$), computed in simple linear regression as $\text{MSE} = s^2 = \frac{\text{SSE}}{n - 2}$.

Standard Error of the Estimate ($s$)

The point estimate of the standard deviation ($\sigma$) of the regression random error term, computed as $s = \sqrt{\text{MSE}}$, representing the typical size of a residual.

Extrapolation

Predicting values of the dependent variable ($Y$) using values of the independent variable ($X$) that fall outside the observed experimental region of the data, producing unreliable estimates.

Lurking Variable

An unmeasured or omitted variable that simultaneously affects both the independent and dependent variables, creating a misleading or phantom association between them.

Constant Variance Assumption

The regression requirement that the error terms have identical spread across all values of $X$, violated when residual plots fan out (increasing variance) or funnel in (decreasing variance).

Independence Assumption

The regression requirement that error terms are statistically independent of one another, most commonly violated by time-series data displaying cyclical patterns, runs, or waves over time.

Multiple Linear Regression Model

A regression model relating a single dependent variable ($y$) to two or more independent variables ($x_1, x_2, \dots, x_k$), formulated as $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \dots + \beta_k x_k + \varepsilon$.

Partial Regression Slope ($b_j$)

The estimated change in the mean value of $y$ resulting from a one-unit increase in $x_j$, holding all other independent variables in the model constant.

Adjusted $R^2$

A modified version of $R^2$ that penalizes models for the inclusion of unnecessary independent variables, used to compare the explanatory power of regression models with different numbers of predictors.

Overall $F$-Test (Multiple Regression)

A statistical hypothesis test assessing the overall utility of a regression model by testing $H_0: \beta_1 = \beta_2 = \dots = \beta_k = 0$ against $H_a: \text{at least one } \beta_j \neq 0$ using $F = \frac{\text{MSR}}{\text{MSE}}$.

Dummy Variable

A binary indicator variable coded as $0$ or $1$ used to incorporate qualitative or categorical predictors into a regression equation, where $k$ categories require $k - 1$ dummy variables.

Multicollinearity

A condition in multiple regression where two or more independent variables are highly correlated with each other (indicated by correlations $> 0.9$ or a Variance Inflation Factor $\text{VIF} > 10$), inflating coefficient standard errors.