Linear Regression Models and Residuals

Front

What are residuals in linear regression?

Back

Residuals are the difference between the observed response and the values predicted by the model.

Front

How is the relationship between x and y described in a strong negative correlation?

Back

In a strong negative correlation, as x increases, y tends to decrease significantly.

Tags

CCSS.HSF-LE.A.1B

Front

True or False: A scatter plot and a residual plot are the same thing.

Back

False

Tags

CCSS.HSS.ID.B.6B

Front

How do you calculate a residual?

Back

Residual = Observed - Predicted

Front

What does the slope in a linear regression equation represent?

Back

The slope represents the change in the response variable for each one-unit change in the predictor variable.

Tags

CCSS.HSF.LE.B.5

Front

What is the formula for a linear regression equation?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate in a linear regression model?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Tags

CCSS.HSF.LE.B.5

Front

What does a negative slope indicate in a linear regression model?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Tags

CCSS.HSF.LE.B.5

Front

What is the purpose of a residual plot?

Back

A residual plot is used to assess the fit of a regression model by showing the residuals on the vertical axis and the independent variable on the horizontal axis.

Front

What does it mean if residuals are randomly scattered around zero?

Back

It indicates that the linear regression model is a good fit for the data.