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| + | ===Simple Linear Regression=== | ||
| + | <!-- [[File:SimpleLinearRegression.png|350px|thumb|center|]] --> | ||
| + | [[File:SimpleLinearRegression2.png|600px|center|]] | ||
| + | |||
| + | |||
| + | The purpose of regression analysis is to: | ||
| + | * Predict the value of the dependent variable as a function of the value(s) of at least one independent variable. | ||
| + | * Explain how changes in an independent variable are manifested in the dependent variable | ||
| + | :* The dependent variable is the variable that is to be predicted unexplained. | ||
| + | :* An independent variable is the variable or variables that is used to predict or explain the dependent variable | ||
| + | |||
| + | |||
| + | '''The regression equation:''' | ||
| + | <math> y = a + bx </math> | ||
| + | |||
| + | * Dependent variable: <math> y </math>: | ||
| + | * Independent variable: <math> x </math>: | ||
| + | * Slope: <math> b = r \frac{S_y}{S_x}</math> | ||
| + | : The slope is the amount of change in units of <math>y</math> for each unitchange in <math>x</math>. | ||
| + | * <math> y </math> intercept: <math> a = \bar{y} - b\bar{x} </math>: | ||
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| + | |||
| + | <br /> | ||
Revision as of 21:25, 23 December 2020
Simple Linear Regression
The purpose of regression analysis is to:
- Predict the value of the dependent variable as a function of the value(s) of at least one independent variable.
- Explain how changes in an independent variable are manifested in the dependent variable
- The dependent variable is the variable that is to be predicted unexplained.
- An independent variable is the variable or variables that is used to predict or explain the dependent variable
The regression equation:
- Dependent variable: :
- Independent variable: :
- 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 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} } :
