Stats Unit 3

Independent variable

A variable that has no relationship to another variable, often considered as the cause in an experiment.

Association

A statistical term indicating that there is a relationship between two variables, but it does not imply causation.

Correlation

A statistical measurement that describes the linear relationship between two variables, showing how one variable may change with respect to another.

Causation

The relationship in which one variable directly causes a change in another variable, indicating a cause-and-effect scenario.

Descriptors of a scatter plot

The key characteristics used to analyze a scatter plot, which include direction, form, strength, and any unusual features.

Direction in scatter plots

Refers to whether the correlation between two variables is positive (both increase together) or negative (one increases while the other decreases).

Form vs. Strength in scatter plots

Form describes the type of relationship (linear or nonlinear), while strength indicates the degree of correlation, quantified as strong, moderate, or weak.

Strength in correlation

The degree of association between two variables quantified as strong (|r| >= .8), moderate (.5 < |r| < .8), or weak (|r| < .5).

Residual

The vertical distance between an actual data point and the corresponding point on the regression line, indicating the error of prediction.

Line of best fit

A straight line drawn through a scatter plot that best represents the data points, minimizing the distances between itself and the points to express the overall trend.

Equation for line of best fit

The mathematical formula represented as y^ = a + bx, where y^ is the predicted value, a is the y-intercept, and b is the slope of the line.

Slope of the regression line

A value that indicates the rate of change in the dependent variable (y) for every one unit increase in the independent variable (x).

Y-intercept

The point where the regression line crosses the y-axis, representing the expected value of y when the independent variable x is zero.

Interpolation vs. Extrapolation

Interpolation refers to estimating values within the range of available data, whereas extrapolation involves predicting values outside the available data range.

Outlier

A data point that significantly deviates from the other observations in a dataset, often affecting the results of regression analysis.

Coefficient of determination

Symbolized as R^2, it quantifies how well the regression model explains the variability in the dependent variable, expressed as a percentage.

Correlation coefficient

A numerical value that assesses the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

Conditions for categorical predictors

Assumptions required for the validity of a statistical model that uses categorical predictors, including linearity, independence of observations, normality of residuals, and equal variance among groups.

Confounding variable

A variable that influences both the independent variable and the dependent variable, obscuring the true relationship between them.

Lurking variable

An unseen variable that has an influence on both the independent and dependent variables in an analysis, potentially causing misleading conclusions.

Residual by X Plot

A graphical representation used to evaluate the distribution of residuals in relation to the independent variable, aiding in the diagnostic process of regression analysis.

Predicted Plot

A graph that compares actual values to predicted values, providing insights into how well the regression model fits the data.

Quantile Plot

A tool used to assess whether the residuals of a model follow a normal distribution, which is important for validating regression model assumptions.