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

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Question

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

Answer

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.

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Question

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?

Answer

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 $s_{y}$ .

$b_{1} = r\frac{s_{y}}{s_{x}}$
$\frac{b_{1}}{r} = \frac{s_{y}}{s_{x}}$
$s_{y} = \frac{b_{1}}{r}{s_{x}} = \frac{-7}{-1}2 = 7\cdot 2 = 14$

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Question

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

Answer

Use the formula $\beta _1 = r\frac{s_y}{s_x}$ .

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

$0.64 = 0.8\frac{s_y}{5}$

$0.8 = \frac{s_y}{5}$

$s_y = 0.8\cdot 5 = 4$

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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 $s_{y}$ .

$b_{1} = r\frac{s_{y}}{s_{x}}$
$\frac{b_{1}}{r} = \frac{s_{y}}{s_{x}}$
$s_{y} = \frac{b_{1}}{r}{s_{x}} = \frac{-7}{-1}2 = 7\cdot 2 = 14$

Compare your answer with the correct one above

Question

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

Answer

Use the formula $\beta _1 = r\frac{s_y}{s_x}$ .

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

$0.64 = 0.8\frac{s_y}{5}$

$0.8 = \frac{s_y}{5}$

$s_y = 0.8\cdot 5 = 4$

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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 $s_{y}$ .

$b_{1} = r\frac{s_{y}}{s_{x}}$
$\frac{b_{1}}{r} = \frac{s_{y}}{s_{x}}$
$s_{y} = \frac{b_{1}}{r}{s_{x}} = \frac{-7}{-1}2 = 7\cdot 2 = 14$

Compare your answer with the correct one above

Question

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

Answer

Use the formula $\beta _1 = r\frac{s_y}{s_x}$ .

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

$0.64 = 0.8\frac{s_y}{5}$

$0.8 = \frac{s_y}{5}$

$s_y = 0.8\cdot 5 = 4$

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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 $s_{y}$ .

$b_{1} = r\frac{s_{y}}{s_{x}}$
$\frac{b_{1}}{r} = \frac{s_{y}}{s_{x}}$
$s_{y} = \frac{b_{1}}{r}{s_{x}} = \frac{-7}{-1}2 = 7\cdot 2 = 14$

Compare your answer with the correct one above

Question

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

Answer

Use the formula $\beta _1 = r\frac{s_y}{s_x}$ .

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

$0.64 = 0.8\frac{s_y}{5}$

$0.8 = \frac{s_y}{5}$

$s_y = 0.8\cdot 5 = 4$

Compare your answer with the correct one above

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