Simple Linear Regression

These flashcards cover key vocabulary and concepts from the simple linear regression lecture notes.

Deterministic Models

Models that hypothesize exact relationships where prediction error is negligible.

Probabilistic Models

Models that include both deterministic components and random error in their predictions.

Least Squares Approach

A method to fit a model by minimizing the sum of squared errors.

Correlation Coefficient (r)

A measure of the strength of the linear relationship between two variables, ranging from -1 to +1.

Slope (β1)

The change in the dependent variable (y) for every unit increase in the independent variable (x).

Y-intercept (β0)

The predicted value of y when the independent variable x is zero.

Coefficient of Determination (r²)

Represents the proportion of variance in the dependent variable that can be explained by the independent variable.

Assumptions of Linear Regression

1. Mean of error term is 0, 2. Constant variance of error terms, 3. Normality of error terms, 4. Independence of error terms.

Standard Deviation (s)

An estimate of the variability of the errors in the regression model.

Sum of Squared Errors (SSE)

The sum of the squares of the differences between observed and predicted values.

Expected Value of y (E(y))

The mean value of the dependent variable derived from the deterministic component.

Random Error (ε)

The component of prediction error that accounts for variability due to unforeseen factors.

Sample Correlation Coefficient (r) Formula

Calculated as SS (xy) / sqrt(SS (x) * SS (y)).