Difference between revisions of "Página de pruebas"
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:: The equation is composed of 2 parameters: | :: The equation is composed of 2 parameters: | ||
| − | ::* Slope: <math> b | + | ::* Slope: <math> b </math> |
| − | :: The slope is the amount of change in units of <math>y</math> for each unitchange in <math>x</math>. | + | ::: The slope is the amount of change in units of <math>y</math> for each unitchange in <math>x</math>. |
| − | ::* The <math>y-axis</math> intercept | + | ::* The <math>y-axis</math> intercept: <math> a </math> |
</blockquote> | </blockquote> | ||
Revision as of 20:52, 27 December 2020
Simple Linear Regression
https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s
In general, there are 3 main stages in Linear regression:
- 1. Using Least-squares to fit a line to the data
- 2. Calculating
- 3. Calculating a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle p-value} for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R^2}
- Using Least-squares to fit a line to the data
- First, draw a line through the data.
- Second, calculate the Residual sum of squares: Measure the distance from the line to each data point (residual), square each distance, and then add them up.
- The distance from a line to a data point is called a residual
- Then, we rotate the line a little bit and calculate the RSS. We do this many times.
- ...
- Then, the line that represents the linear regression is the one corresponding to the rotation that has the least RSS. The regression equation:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y = a + bx }
- The equation is composed of 2 parameters:
- Slope: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle b }
- The slope is the amount of change in units of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y} for each unitchange in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x} .
- The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y-axis} intercept: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle a }
The regression equation:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y = a + bx }
- Dependent variable: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y } :
- Independent variable: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x } :
- Slope: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle b = r \frac{S_y}{S_x}}
- The slope is the amount of change in units of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y} for each unitchange in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x} .
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y } intercept: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle a = \bar{y} - b\bar{x} } :
