Answered: The slope of a regression line (y on x)…

The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and SDx=4.0, then the correlation coefficient between the two variables is: A. 0.3 B. -0.3 C. 0.8 D. -0.8

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.

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Question

The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and
SDx=4.0, then the correlation coefficient between the two variables is:
A. 0.3
B. -0.3
C. 0.8
D. -0.8

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Expert Solution

Step 1

The regression line $Y$ on $X$ is as follows.

$y = a + b x$

$b$ is the slope of the regression line.

$a$ is the intercept.

The formula for the slope is as follows.

$b = r \frac{S D_{y}}{S D_{x}}$

$r$ is the correlation coefficient.

The slope of the regression line is -0.24

$S D_{y} = 3.2 S D_{x} = 4.0$

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