How to find the least-squares regression line

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

Questions 1 - 3

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

Dependent, Independent

Independent, Dependent

First, Second

Qualified, Unqualified

Greater, Lesser

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.

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?

Explanation

The key here is to utilize

$b_{1} = r\frac{s_{y}}{s_{x}}$ .

"Perfect negative linear correlation" means , while the rest of the problem indicates $b_{1} = -7$ and $s_{x} = 2$ . This enables us to solve for $s_{y}$ .