R Squared: Difference between revisions
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=Introduction= | =Introduction= | ||
This is all about R² | This is all about R². | ||
=My Thoughts= | |||
==Least Squares Review== | |||
Most of this requires you to think about a dataset with lots of points. What we are trying to do is with [[least squares | least squares]] is find the best fit for a line for our data points. Once we have this we could maybe predict for a new data point what the y-value might be given the x-value. Here is the formula | |||
<br> | |||
<math> | |||
S = \sum_{i=1}^n (y_i - \hat{y}_i)^2 | |||
</math> | |||
<br> | |||
Or in english we have | |||
<math> | |||
((a*x_1 + b) - y_1)^2 + (a*x_2 + y_2)^2 + | |||
</math>... | |||
=What is the difference= | =What is the difference= | ||
Well I guess R² = R squared. R² is the variance between a dependent variable and an independent variable in terms of percentage. Therefore 0.4 R² = 40% and R = 0.2. I guess I agree that using R² does provide an easier way to understand what you mean however there is no sign on R². | Well I guess R² = R squared. R² is the variance between a dependent variable and an independent variable in terms of percentage. Therefore 0.4 R² = 40% and R = 0.2. I guess I agree that using R² does provide an easier way to understand what you mean however there is no sign on R². | ||
Revision as of 01:51, 23 April 2025
Introduction
This is all about R².
My Thoughts
Least Squares Review
Most of this requires you to think about a dataset with lots of points. What we are trying to do is with least squares is find the best fit for a line for our data points. Once we have this we could maybe predict for a new data point what the y-value might be given the x-value. Here is the formula
Or in english we have
...
What is the difference
Well I guess R² = R squared. R² is the variance between a dependent variable and an independent variable in terms of percentage. Therefore 0.4 R² = 40% and R = 0.2. I guess I agree that using R² does provide an easier way to understand what you mean however there is no sign on R².
Formula for R²
This is given by
A reminder of how we calculate variance, we add up the differences from the mean like below. Note this shows a population and we should divide by n-1 not n but I liked the graphic.
This was a nice picture
