Linear models - Revision history

Bosmana fem: /* FEM PAGE CONTRIBUTORS */

2023-04-10T21:47:02Z

FEM PAGE CONTRIBUTORS

← Older revision		Revision as of 21:47, 10 April 2023
Line 26:		Line 26:
	The coefficients β1 and β2 respectively provide estimate of the effect of x1 and x2 which are mutually un-confounded. Mathematically there are no limits to the number of variables to be included in a model.		The coefficients β1 and β2 respectively provide estimate of the effect of x1 and x2 which are mutually un-confounded. Mathematically there are no limits to the number of variables to be included in a model.

	==FEM PAGE CONTRIBUTORS==		<div style="display: inline-block; width: 25%; vertical-align: top; border: 1px solid #000; background-color: #d7effc; padding: 10px; margin: 5px;">
			'''FEM PAGE CONTRIBUTORS 2007'''
	;Editor		;Editor
	: Fernando Simon		: Fernando Simon
Line 35:		Line 36:
	: Lisa Lazareck		: Lisa Lazareck
	: Fernando Simon		: Fernando Simon
			</div>


	[[Category:Logistic Regression]]		[[Category:Logistic Regression]]

Bosmana fem at 10:39, 25 March 2023

2023-03-25T10:39:01Z

← Older revision		Revision as of 10:39, 25 March 2023
Line 26:		Line 26:
	The coefficients β1 and β2 respectively provide estimate of the effect of x1 and x2 which are mutually un-confounded. Mathematically there are no limits to the number of variables to be included in a model.		The coefficients β1 and β2 respectively provide estimate of the effect of x1 and x2 which are mutually un-confounded. Mathematically there are no limits to the number of variables to be included in a model.

			==FEM PAGE CONTRIBUTORS==
			;Editor
			: Fernando Simon
			;Original Author
			: Alain Moren
			;Contributors
			: Arnold Bosman
			: Lisa Lazareck
			: Fernando Simon



	[[Category:Logistic Regression]]		[[Category:Logistic Regression]]

Bosmana fem: /* The straight line */

2023-03-25T10:27:50Z

The straight line

← Older revision		Revision as of 10:27, 25 March 2023
Line 9:		Line 9:
	The equation of a straight line is:		The equation of a straight line is:

	y = β0 + β1x		y = β0 + β1x

	In which		In which

Bosmana fem: /* The straight line */

2023-03-25T10:27:29Z

The straight line

← Older revision		Revision as of 10:27, 25 March 2023
Line 3:		Line 3:

	[[File:3240.Straight.gif-550x0.png\|600px\|frameless\|centre\|Figure 1 shows the relation between y and x]]		[[File:3240.Straight.gif-550x0.png\|600px\|frameless\|centre\|Figure 1 shows the relation between y and x]]
			Figure 1 shows the relation between y and x

	The straight line represents the average values of y for different values of x. It is a regression line. It was obtained by fitting a straight line equation to the data. A simple way to understand how the straight line is fitted on the dot plot is to visually guess where it would need to be placed in order to minimise the various distances between each dot and the line.		The straight line represents the average values of y for different values of x. It is a regression line. It was obtained by fitting a straight line equation to the data. A simple way to understand how the straight line is fitted on the dot plot is to visually guess where it would need to be placed in order to minimise the various distances between each dot and the line.

Bosmana fem: /* The straight line */

2023-03-25T10:26:53Z

The straight line

← Older revision		Revision as of 10:26, 25 March 2023
Line 2:		Line 2:
	Mathematical models can be as simple as a straight line. In a linear model the straight line is used to describe the relation between two variables. We express y according to the value of x. We predict y according to x. Therefore x is called the predictor or independent variable and y the predicted or dependent variable.		Mathematical models can be as simple as a straight line. In a linear model the straight line is used to describe the relation between two variables. We express y according to the value of x. We predict y according to x. Therefore x is called the predictor or independent variable and y the predicted or dependent variable.

	[[File:3240.Straight.gif-550x0.png\|~~400px~~\|frameless\|~~left~~\|Figure 1 shows the relation between y and x]]		[[File:3240.Straight.gif-550x0.png\|600px\|frameless\|centre\|Figure 1 shows the relation between y and x]]

Bosmana fem: /* The straight line */

2023-03-25T10:25:50Z

The straight line

← Older revision		Revision as of 10:25, 25 March 2023
Line 2:		Line 2:
	Mathematical models can be as simple as a straight line. In a linear model the straight line is used to describe the relation between two variables. We express y according to the value of x. We predict y according to x. Therefore x is called the predictor or independent variable and y the predicted or dependent variable.		Mathematical models can be as simple as a straight line. In a linear model the straight line is used to describe the relation between two variables. We express y according to the value of x. We predict y according to x. Therefore x is called the predictor or independent variable and y the predicted or dependent variable.

	~~Figure 1 shows the relation between y and x.~~		[[File:3240.Straight.gif-550x0.png\|400px\|frameless\|left\|Figure 1 shows the relation between y and x]]
	[[File:3240.Straight.gif-550x0.png\|~~300px~~\|~~frame~~]]

Bosmana fem: /* The straight line */

2023-03-25T10:24:22Z

The straight line

← Older revision		Revision as of 10:24, 25 March 2023
Line 3:		Line 3:

	Figure 1 shows the relation between y and x.		Figure 1 shows the relation between y and x.
			[[File:3240.Straight.gif-550x0.png\|300px\|frame]]

Bosmana fem at 10:23, 25 March 2023

2023-03-25T10:23:19Z

← Older revision		Revision as of 10:23, 25 March 2023
Line 1:		Line 1:
			==The straight line==
			Mathematical models can be as simple as a straight line. In a linear model the straight line is used to describe the relation between two variables. We express y according to the value of x. We predict y according to x. Therefore x is called the predictor or independent variable and y the predicted or dependent variable.

			Figure 1 shows the relation between y and x.



			The straight line represents the average values of y for different values of x. It is a regression line. It was obtained by fitting a straight line equation to the data. A simple way to understand how the straight line is fitted on the dot plot is to visually guess where it would need to be placed in order to minimise the various distances between each dot and the line.

			The equation of a straight line is:

			y = β0 + β1x

			In which

			β0 is the intercept (value of y when x = 0)

			β1x is the coefficient of x. It describes the slope of the line. It represents the number of units of change in y when x increases by 1 unit.

			==The general linear model==
			Let's suppose that in the above example we want to predict y not only according to x1 but also according to x2. We would have then two predictors. The relation between x1 , x2 and y is still a straight line. The equation is now:

			y = β0 + β1x1 + β2x2

			To locate the straight line in the dots we need to imagine a 3 dimensional rectangle coordinates with y expressed according to x1 and x2.

			The coefficients β1 and β2 respectively provide estimate of the effect of x1 and x2 which are mutually un-confounded. Mathematically there are no limits to the number of variables to be included in a model.




	[[Category:Logistic Regression]]		[[Category:Logistic Regression]]

Bosmana fem: Created page with " Category:Logistic Regression"

2023-03-23T11:27:10Z

Created page with " Category:Logistic Regression"

New page

[[Category:Logistic Regression]]