# Simple Linear Regression Flashcards

Regression analysis

Regression analysis is used to:

predict the value of a dependent variable (Y) based on the value of at least one independent variable (X)

explain the impact of changes in an independent variable on the dependent variable

Dependent variable (y)

Dependent variable (Y): the variable we wish to predict or explain (response variable)

Independent variable (x)

Independent variable (X): the variable used to explain the dependent variable (explanatory variable)

Simple linear regression

Only one independent variable, X

Relationship between X and Y is described by a linear function

Changes in Y are assumed to be caused by changes in X

b0 and b1

b0 and b1 are obtained by finding the values of b0 and b1 that minimise the sum of the squared differences between actual values (Y) and predicted values ( )

b0

b0 is the estimated average value of Y when the value of X is zero

b1

b1 is the estimated change in the average value of Y as a result of a one-unit change in X

SST

Total Sum of Squares

Measures the variation of the Yi values around their mean Y

SSR

Regression Sum of Squares

Explained variation attributable to the relationship between X and Y

SSE

Error Sum of Squares

Variation attributable to factors other than

the relationship between X and Y

Coefficient of Determination, r2

The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variable

The coefficient of determination is also called r-squared and is denoted as r2

ASSUMPTIONS OF REGRESSION

Linearity

Independence of errors

Normality of errors

Equal variance

Linearity

The underlying relationship between X and Y is linear

Independence of errors

Error values are statistically independent

Normality of errors

Error values (ε) are normally distributed for any given value of X