AP Statistics : How to find the least-squares regression line

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #8 : Bivariate Data

In a regression analysis, the y-variable should be the ___________ variable, and the x-variable should be the ___________ variable.

Possible Answers:

Greater, Lesser

First, Second

Qualified, Unqualified

Dependent, Independent

Independent, Dependent

Correct answer:

Dependent, Independent

Explanation:

Regression tests seek to determine one variable's ability to predict another variable.  In this analysis, one variable is dependent (the one predicted), and the other is independent (the variable that predicts).  Therefore, the dependent variable is the y-variable and the independent variable is the x-variable.

Example Question #1 : How To Find The Least Squares Regression Line

If a data set has a perfect negative linear correlation, has a slope of  and an explanatory variable standard deviation of , what is the standard deviation of the response variable?

Possible Answers:

Correct answer:

Explanation:

The key here is to utilize

.

"Perfect negative linear correlation" means , while the rest of the problem indicates  and . This enables us to solve for .



Example Question #3 : How To Find The Least Squares Regression Line

A least-squares regression line has equation  and a correlation of . It is also known that . What is ?

Possible Answers:

Correct answer:

Explanation:

Use the formula .

Plug in the given values for and and this becomes an algebra problem.

 

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