what is the slope of regression line

by Kiera Bins Published 3 years ago Updated 2 years ago

The Equation of the Regression Line

If r = 0, the regression line is horizontal: Its slope is zero.
If r = 1, all the points fall on a line with positive slope. The regression line and the SD line are the same.
If r = −1, all the points fall on a line with negative slope. The regression line and the SD line are the same.

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

Full Answer

How to find a linear regression slope?

How to Calculate Linear Regression Slope? The formula of the LR line is Y = a + bX.Here X is the variable, b is the slope of the line and a is the intercept point. So from this equation we can do back calculation and find the formula of the slope.

How do you calculate the slope of a regression equation?

The mean of the x values
The mean of the y values
The standard deviation of the x values (denoted sx)
The standard deviation of the y values (denoted sy)
The correlation between X and Y (denoted r)

How to find and apply the slope of a line?

To find the slope by hand, follow the next steps:

Insert the coordinates (xA,yA) ( x A, y A) and (xB,yB) ( x B, y B). ...
Subtract the second coordinates and first coordinates, this gives us yB − yA = 1− 5 = −4 y B − y A = 1 − 5 = − 4 ...
Simplify the fraction to get the slope of 4 7 4 7.

How to test the significance of a regression slope?

slope.test: One-sample test of a (standardised) major axis slope

Description. Test if the slope of a major axis or standardised major axis equals a specific value. ...
Usage
Arguments. Use with () instead (see Examples). ...
Value. The P-value, taken from the F-distribution. ...
Details. Tests if the line relating y to x has a slope equal to test.value (which has a default value of 1). ...
References. Warton D. ...
See Also
Examples

Need more help understanding slope of regression line?

The data in the accompanying table are returns of 50 hedge funds reported for the month of December 2005. The returns are computed as the change in value of assets managed by the fund during the month divided by the ...

Get the most out of Chegg Study

In math there are many key concepts and terms that are crucial for students to know and understand. Often it can be hard to determine what the most important math concepts and terms are, and even once you’ve identified them you still need to understand what they mean.

How to Interpret the Slope of a Least-Squares Regression Line

Step 1: Identify the slope. This is the quantity attached to x in a regression equation, or the "Coef" value in a computer read out in the same row as the variable itself (the one not marked constant).

What Are Least-Square Regression Lines and their Slopes?

Least-Squares Regression Line: The line of best fit to link two variables in a dataset. Given a specific data set that shows some amount of linkage between two variables, we can construct a line to estimate the relationship between the two.

Example of Interpreting the Slope from a Least-Squares Regression Equation

Sajant's computer has been slowing down during the peak of summer, so he started measuring the temperature of the room in degrees Fahrenheit and the boot time of his computer in seconds, once a week for a year.

Example of Interpreting the Slope from a Least-Squares Regression Computer Output

Phanalla Incorporated is investigating reports that extended ownership of their phones is reducing life spans. They've collected data from a group of now deceased individuals, on how many months they owned a Phanalla phone, and their lifespan in years. The following computer output is produced for the least-squares regression line

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