Ch. 14: Correlation and Regression

Correlation

A statistical measure that shows the strength and direction of a relationship between two variables

Scatter plot

A graph showing individual data points plotted to display the relationship between two variables

Positive correlation

A correlation of +1.00 or -1.00, meaning every pair of scores follows an exact straight-line pattern

Envelope

The overall shape or boundary formed by the outermost points in a scatter plot

Pearson correlation

A correlation that measures linear relationships between two continuous variables

Linear relationship

A relationship where data points follow a straight-line pattern

Sum of products (SP)

A value used in correlation and regression that reflects how two variables vary together

SP definitional formula

The formula SP that uses deviation scores (x-M)(y-M)

SP computational formula

A shortcut formula for SP that uses sums of X, sums of Y, and sums of XY

Outliers

Scores that are extremely different from the rest of the data and can distort correlations

Restricted range

When one or both variables don’t cover their full possible values, which weakens the coorelation

Coefficient of determination (r²)

The proportion of variability in one variable that can be explained by the other

Coorelation matrix

A table showing all the coorelation coefficients among multiple variables

Spearman coorelation

A coorelation used for rank-ordered data or to measure monotonic relationships

Monotonic relationship

A relationship where variables move consistently in one direction but not necessarily in a straight line

Point-biserial coorelation

A coorelation between on continuous variable and one true dichotomous variable (e.g., male/female)

Dichotomous (binomial) variable

A variable with only two possible categories, such as yes/no

Phi-coefficient

A coorelation used when both variables are dichotomous

Linear equation

An equation that describes a straight-line relationship between X and Y

Slope

The amount Y changes for each one-unit change in X

Y-intercept

The value of Y when X equals zero

Regression

A statistical method used to predict one variable from another

Regression line

The straight line that best represents the relationship between two variables

Least-squared-error solution

The metod that chooses the regression line that minimizes the total squared distance between the line and actual data points

Regression equation for Y

The formula used to predict Y from X: ^ on top of Y = bx+a

Standardized form of the regression formula

A version of the regression equation using z-scores instead of raw scores

Standard error of estimate

A measure of how much actual scores differ from the predicted scores on average

Predicted variability (SS regression)

The portion of total variability in Y that is explained by the regression model

Unpredicted variability (SS residual)

The portion of Y’s variability that the regression model cannot explain

Analysis of regression

An ANOVA procedure used to test whether the regression model significantly predicts the outcome