Difference between revisions of "Página de pruebas"
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: '''2. Calculating <math>R^2</math>''' | : '''2. Calculating <math>R^2</math>''' | ||
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| − | In the | + | In the following example, they are using different terminology to the one that we saw in Section [[Data_Science#The_coefficient_of_determination_R.5E2]] |
It is very important to note how the result of <math>R^2</math>. In our example <span style='color: red'>''' There is a 60% reduction in variance when we take the mouse weight into account '''</span> or <span style='color: red'>''' Mouse weight "explains" 60% of the variation in mouse size. '''</span> | It is very important to note how the result of <math>R^2</math>. In our example <span style='color: red'>''' There is a 60% reduction in variance when we take the mouse weight into account '''</span> or <span style='color: red'>''' Mouse weight "explains" 60% of the variation in mouse size. '''</span> | ||
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| + | [[File:Linear_regression2.png|600px|thumb|center|Takinf from https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s]] | ||
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</blockquote> | </blockquote> | ||
Revision as of 21:31, 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 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}
- 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}
- 1. 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:
- 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 }
- 2. Calculating 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}
In the following example, they are using different terminology to the one that we saw in Section Data_Science#The_coefficient_of_determination_R.5E2
It is very important to note how the result 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 R^2} . In our example There is a 60% reduction in variance when we take the mouse weight into account or Mouse weight "explains" 60% of the variation in mouse size.
