Mathematics/Statistics/Regression Lines - Revision history

Brodriguez: Brodriguez moved page Statistics/Regression Lines to Mathematics/Statistics/Regression Lines

2020-10-25T17:21:37Z

Brodriguez moved page Statistics/Regression Lines to Mathematics/Statistics/Regression Lines

← Older revision

Revision as of 17:21, 25 October 2020

Brodriguez: Move correlation coefficient to separate page

2020-05-18T06:56:53Z

Move correlation coefficient to separate page

@@ Line 6: / Line 6: @@
 Since this is regression line is a standard straight line, it can be represented by a standard {{ ic | <math>y = mx + b</math>}} equation.
@@ Line 51: / Line 34: @@
   <math>m = r \frac{S_y}{S_x}</math>
 Where
-* <math>r</math> is the [[#Correlation Coefficients|correlation coefficient]] for our dataset.
+* <math>r</math> is the [[Statistics/Correlation Coefficients|correlation coefficient]] for our dataset.
 * <math>S_y</math> is the [[Statistics/Core_Measurements#Standard Deviation|standard deviation]] of our x.
 * <math>S_x</math> is the [[Statistics/Core_Measurements#Standard Deviation|standard deviation]] of our y.

Brodriguez: Create regression equation section

2020-05-18T06:23:27Z

Create regression equation section

@@ Line 6: / Line 6: @@
 Since this is regression line is a standard straight line, it can be represented by a standard {{ ic | <math>y = mx + b</math>}} equation.
 == Residuals ==
@@ Line 16: / Line 34: @@
-We can then take this a step further and combine all residuals in our dataset to get an overal view of "how closely the regression line matches our dataset".
+We can then take this a step further and combine all residuals in our dataset to get an overall view of "how closely the regression line matches our dataset".
   <math>\sum_{i=1}^n (r_i)^2</math>
@@ Line 23: / Line 41: @@
 == Least Squares Regression ==
-'''Least Squares Regression''' is one of the more popular ways to minimize the sum of all residuals in our dataset.
+'''Least Squares Regression''' is one of the more popular ways to minimize the sum of all residuals in our dataset. We can calculate this regression line with a few steps:

Brodriguez: Create page

2020-05-17T23:23:49Z

Create page

New page

{{ ToDo | Add images/graphs to help describe page. }}

A regression line is effectively an attempt to fit some data to a straight line.

Basically, given some set of data points, you create a line that as closely as possible fits the data. This is accomplished by trying to minimize the total distance between all points and the line itself.

Since this is regression line is a standard straight line, it can be represented by a standard {{ ic | <math>y = mx + b</math>}} equation.

== Residuals ==
Given a single data point, a '''residual''' is the distance between that single point and the regression line.

A positive residual value indicates that the data point is somewhere above the regression line. A negative residual value indicates that the data point is somewhere below the regression line. Larger values indicate the point is farther away.

To calculate the residual for some point at <math>(p_x, p_y)</math>, we have the following equation for some <math>m</math> and <math>b</math> from our regression line:
<math>residual_p = p_y - (m(p_x) + b)</math>

We can then take this a step further and combine all residuals in our dataset to get an overal view of "how closely the regression line matches our dataset".
<math>\sum_{i=1}^n (r_i)^2</math>

Squaring means means that negative residual values don't cancel out positive values. It also means points that are farther away from the line end up with more weight than points closer to the line.

== Least Squares Regression ==
'''Least Squares Regression''' is one of the more popular ways to minimize the sum of all residuals in our dataset.