Template:Least Squares/Rank Regression Equations - Revision history

Lisa Hacker: Replaced content with 'Category: For Deletion'

2012-07-20T12:27:43Z

Replaced content with 'Category: For Deletion'

Harry Guo: moved Least Squares/Rank Regression Equations to Template:Least Squares/Rank Regression Equations: Use it in Weibull Appendix

2012-02-06T22:25:22Z

moved Least Squares/Rank Regression Equations to Template:Least Squares/Rank Regression Equations: Use it in Weibull Appendix

← Older revision	Revision as of 22:25, 6 February 2012
(No difference)

Pantelis at 14:14, 29 October 2011

2011-10-29T14:14:59Z

← Older revision		Revision as of 14:14, 29 October 2011
Line 1:		Line 1:
	{{template:~~LDABOOK~~\|4A\|~~Least Squares/Rank Regression Equations~~}}		{{template:LDAOtherSections\|\|}}

Pantelis: /* Illustrating with an Example */

2011-10-29T13:50:11Z

Illustrating with an Example

← Older revision		Revision as of 13:50, 29 October 2011
Line 203:		Line 203:
	The plotted line is shown in the next figure.		The plotted line is shown in the next figure.

	[[Image:LdaappendixA.1.gif\|thumb\|center\|~~400px~~]]		[[Image:LdaappendixA.1.gif\|thumb\|center\|500px]]

	For rank regression on X (RRX) using the same table yields:		For rank regression on X (RRX) using the same table yields:

Pantelis: /* Illustrating with an Example */

2011-10-29T13:49:42Z

Illustrating with an Example

← Older revision		Revision as of 13:49, 29 October 2011
Line 222:		Line 222:
	The plotted line is shown in the next figure.		The plotted line is shown in the next figure.

	[[Image:LdaappendixA.2.gif\|thumb\|center\|~~400px~~]]		[[Image:LdaappendixA.2.gif\|thumb\|center\|500px]]

	Note that the regression on Y is not necessarily the same as the regression on X. The only time when the two regressions are the same (i.e. will yield the same equation for a line) is when the data lie perfectly on a line.		Note that the regression on Y is not necessarily the same as the regression on X. The only time when the two regressions are the same (i.e. will yield the same equation for a line) is when the data lie perfectly on a line.

Pantelis: /* Illustrating with an Example */

2011-10-29T13:48:59Z

Illustrating with an Example

← Older revision		Revision as of 13:48, 29 October 2011
Line 187:		Line 187:
	<br>		<br>

	From the table then		From the table then, and for rank regression on Y (RRY):

	::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{550.25-(56.5)^2/8}</math>		::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{550.25-(56.5)^2/8}</math>
Line 205:		Line 205:
	[[Image:LdaappendixA.1.gif\|thumb\|center\|400px]]		[[Image:LdaappendixA.1.gif\|thumb\|center\|400px]]

	For rank regression on X using the same table yields:		For rank regression on X (RRX) using the same table yields:

	::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{276.25-(41.5)^2/8}</math>		::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{276.25-(41.5)^2/8}</math>

Pantelis: /* Illustrating with an Example */

2011-10-29T13:47:12Z

Illustrating with an Example

← Older revision		Revision as of 13:47, 29 October 2011
Line 205:		Line 205:
	[[Image:LdaappendixA.1.gif\|thumb\|center\|400px]]		[[Image:LdaappendixA.1.gif\|thumb\|center\|400px]]

	For rank regression on X using the ~~analyzed data in Table A.1, Eqns. (8) and (7) yield~~:		For rank regression on X using the same table yields:

	::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{276.25-(41.5)^2/8}</math>		::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{276.25-(41.5)^2/8}</math>

Pantelis: /* Illustrating with an Example */

2011-10-29T13:46:31Z

Illustrating with an Example

← Older revision		Revision as of 13:46, 29 October 2011
Line 187:		Line 187:
	<br>		<br>

	~~Using~~ the ~~results in Table A.1, Eqns. (3) and (4) yield:~~		From the table then

	::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{550.25-(56.5)^2/8}</math>		::<math>\widehat{b}=\frac{387.5-(56.5)(41.5)/8}{550.25-(56.5)^2/8}</math>

Pantelis: /* Illustrating with an Example */

2011-10-29T13:39:47Z

Illustrating with an Example

← Older revision		Revision as of 13:39, 29 October 2011
Line 122:		Line 122:
	\|-		\|-
	! scope="row" \| 1		! scope="row" \| 1
	\| align="~~right~~" 1		\| align="center" \| 1
	\| align="~~right~~" 1.5		\| align="center" \| 1.5
	\| align="~~right~~" 1		\| align="center" \| 1
	\| 1.5		\| align="center" \|1.5
	\| 2.25		\| align="center" \|2.25
	\|-		\|-
	! scope="row" \| 2		! scope="row" \| 2
	\| 2.5		\|align="center" \| 2.5
	\| 2		\|align="center" \| 2
	\| 6.25		\|align="center" \| 6.25
	\| 5		\|align="center" \| 5
	\| 4		\|align="center" \| 4
	\|-		\|-
	! scope="row" \| 3		! scope="row" \| 3
	\| 4		\| align="center" \|4
	\| 4		\|align="center" \| 4
	\| 16		\| align="center" \|16
	\| 16		\| align="center" \|16
	\| 16		\| align="center" \|16
	\|-		\|-
	! scope="row" \| 4		! scope="row" \| 4
	\| 6		\|align="center" \| 6
	\| 4		\| align="center" \|4
	\| 36		\| align="center" \|36
	\| 24		\| align="center" \|24
	\| 16		\| align="center" \|16
	\|-		\|-
	! scope="row" \| 5		! scope="row" \| 5
	\| 8		\| align="center" \|8
	\| 5		\| align="center" \|5
	\| 64		\| align="center" \|64
	\| 40		\| align="center" \|40
	\| 25		\| align="center" \|25
	\|-		\|-
	! scope="row" \| 6		! scope="row" \| 6
	\| 9		\| align="center" \|9
	\| 7		\| align="center" \|7
	\| 81		\| align="center" \|81
	\| 63		\| align="center" \|63
	\| 49		\| align="center" \|49
	\|-		\|-
	! scope="row" \| 7		! scope="row" \| 7
	\| 11		\| align="center" \|11
	\| 8		\| align="center" \|8
	\| 121		\| align="center" \|121
	\| 88		\| align="center" \|88
	\| 64		\| align="center" \|64
	\|-		\|-
	! scope="row" \| 8		! scope="row" \| 8
	\| 15		\| align="center" \|15
	\| 10		\| align="center" \|10
	\| 225		\| align="center" \|225
	\| 150		\| align="center" \|150
	\| 100		\| align="center" \|100
	\|-		\|-
	! scope="row" \| <math>\Sigma</math>		! scope="row" \| <math>\Sigma</math>
	\| 56.5		\| align="center" \|56.5
	\| 41.5		\| align="center" \|41.5
	\| 550.25		\| align="center" \|550.25
	\| 387.5		\| align="center" \|387.5
	\| 276.25		\| align="center" \|276.25
	\|}		\|}

Pantelis at 13:35, 29 October 2011

2011-10-29T13:35:46Z

← Older revision		Revision as of 13:35, 29 October 2011
Line 81:		Line 81:
	Fit a least squares straight line using regression on X and regression on Y to the following data:		Fit a least squares straight line using regression on X and regression on Y to the following data:

			<br>

	{\| align="center" border="0" cellspacing="5" width="300" cellpadding="5"		{\| align="center" border="0" cellspacing="5" width="300" cellpadding="5"
Line 106:		Line 106:
	\|}		\|}

			<br>

	The first step is to generate the following table:		The first step is to generate the following table:

			<br>

	{\| align="center" border="1" cellpadding="5" cellspacing="1" width="350"		{\| align="center" border="1" cellpadding="5" cellspacing="1" width="350"
Line 122:		Line 122:
	\|-		\|-
	! scope="row" \| 1		! scope="row" \| 1
	\| 1		\| align="right" 1
	\| 1.5		\| align="right" 1.5
	\| 1		\| align="right" 1
	\| 1.5		\| 1.5
	\| 2.25		\| 2.25
Line 185:		Line 185:
	\|}		\|}

			<br>

	Using the results in Table A.1, Eqns. (3) and (4) yield:		Using the results in Table A.1, Eqns. (3) and (4) yield: