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line that measures the slope between dependent and independent variables

Q: What is the line of regression?

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on the lineGiven a linear regression equation of = 20 - 1.5x, where will the point (3, 15) fall with respect to the regression line?Below the line

Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".

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The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.

Related questions

(mean x, mean y) is always on the regression line.

There are two regression lines if there are two variables - one line for the regression of the first variable on the second and another line for the regression of the second variable on the first. If there are n variables you can have n*(n-1) regression lines. With the least squares method, the first of two line focuses on the vertical distance between the points and the regression line whereas the second focuses on the horizontal distances.

on the lineGiven a linear regression equation of = 20 - 1.5x, where will the point (3, 15) fall with respect to the regression line?Below the line

by regrsioning it.

Linear Regression is a method to generate a "Line of Best fit" yes you can use it, but it depends on the data as to accuracy, standard deviation, etc. there are other types of regression like polynomial regression.

yes.

Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".

It is often called the "Least Squares" line.

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The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.

The point lies 1 unit below the regression line.