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[[File:Linear_regression2.png|600px|thumb|right|Takinf from https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s]] | [[File:Linear_regression2.png|600px|thumb|right|Takinf from https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s]] | ||
| − | In the above example, they are using different terminology to the one that we saw in Section | + | In the above example, they are using different terminology to the one that we saw in Section |
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> | ||
Revision as of 21:30, 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:
- 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 }
- 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 above example, they are using different terminology to the one that we saw in Section
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.
