Linear Regression Models and Residuals

Front

What is a linear regression model?

Back

A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What does the slope in a linear regression equation represent?

Back

The slope indicates the change in the dependent variable for a one-unit change in the independent variable.

Front

What is a residual in the context of linear regression?

Back

The difference between the observed value and the predicted value from the regression model.

Front

What does a positive residual indicate?

Back

It indicates that the predicted value is too small compared to the observed value.

Front

What does a negative residual indicate?

Back

It indicates that the predicted value is too large compared to the observed value.

Front

How do you interpret the y-intercept in a linear regression equation?

Back

The y-intercept represents the predicted value of the dependent variable when all independent variables are zero.

Front

What is the purpose of the coefficient of determination (R²) in linear regression?

Back

R² measures the proportion of variance in the dependent variable that can be explained by the independent variable(s).

Front

What does it mean if there is a strong positive correlation between x and y?

Back

It means that as x increases, y tends to also increase significantly.

Front

What does it mean if there is a weak negative correlation between x and y?

Back

It means that there is a slight tendency for y to decrease as x increases, but the relationship is not strong.

Front

How can you predict a value using a linear regression equation?

Back

Substitute the value of the independent variable into the regression equation to calculate the predicted value of the dependent variable.