Linear Regression Models and Residuals

Front

What is a linear regression model?

Back

A linear regression model is 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 represents the rate of change of the dependent variable for each unit increase in the independent variable.

Front

What is a residual in the context of linear regression?

Back

A residual is the difference between the observed value and the predicted value from a regression model.

Front

What does a random residual plot indicate?

Back

A random residual plot indicates that the linear regression model is a good fit for the data, as there are no patterns in the residuals.

Front

What is the purpose of a residual plot?

Back

The purpose of a residual plot is to assess the goodness of fit of a regression model by examining the residuals.

Front

How do you calculate a residual?

Back

Residual = Observed value - Predicted value.

Front

What does it mean if residuals increase as the independent variable increases?

Back

It may indicate that the linear model is not appropriate, suggesting a non-linear relationship.

Front

What is the significance of the y-intercept in a linear regression equation?

Back

The y-intercept represents the predicted value of the dependent variable when the independent variable is zero.

Front

What is the formula for a simple linear regression equation?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if the residuals are normally distributed?

Back

It suggests that the linear regression model is appropriate and that the errors are random.