Template:Example: Normal Distribution RRX - Revision history

Lisa Hacker: Redirected page to The Normal Distribution

2012-08-13T02:00:33Z

Redirected page to The Normal Distribution

← Older revision		Revision as of 02:00, 13 August 2012
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	~~'''Normal Distribution RRX Example'''~~		#REDIRECT [[The Normal Distribution]]

	~~Using the data of~~ [[~~Normal distribution example 2\|Example 2]] and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.~~

	~~'''Solution'''~~

	The ~~table constructed in [[~~Normal ~~distribution example 2\|Example 2]] applies to this example also. Using the values on this table, we get:~~

	~~::<math>\begin{align}~~
	\hat{b}= & \frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}{{y}_{i}}-\tfrac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}}{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,y_{i}^{2}-\tfrac{{{\left( \underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}} \right)}^{2}}}{14}} \\
	~~\widehat{b}= & \frac{365.2711-(630)(0)/14}{11.3646-{{(0)}^{2}}/14}=32.1411~~
	~~\end{align}</math>~~

	~~and:~~

	~~::<math>\hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}}{14}-\widehat{b}\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}</math>~~

	~~or:~~

	~~::<math>\widehat{a}=\frac{630}{14}-(32.1411)\frac{(0)}{14}=45</math>~~

	~~Therefore:~~

	~~::<math>\widehat{\sigma }=\widehat{b}=32.1411</math>~~

	~~and:~~

	~~::<math>\widehat{\mu }=\widehat{a}=45\text{ hours}</math>~~

	~~The correlation coefficient is obtained as:~~

	~~::<math>\widehat{\rho }=0.979</math>~~

	Note that the results for regression on X are not necessarily the same as the results for regression on Y. 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 straight line.
	~~Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.~~

	~~[[Image:Normal RRX Setting.png\|center\|550px\| ]]~~

	~~The plot of the solution for this example is shown next.~~

	~~[[Image:Normal RRX Plot.png\|center\|550px\|~~ ]]
	~~<math></math>~~

Richard House at 02:32, 8 August 2012

2012-08-08T02:32:27Z

← Older revision		Revision as of 02:32, 8 August 2012
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	Using the data of [[Normal distribution example 2\|Example 2]] and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.		Using the data of [[Normal distribution example 2\|Example 2]] and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.


	'''Solution'''		'''Solution'''
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	::<math>\widehat{\rho }=0.979</math>		::<math>\widehat{\rho }=0.979</math>

	Note that the results for regression on X are not necessarily the same as the results for regression on Y. 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 straight line.		Note that the results for regression on X are not necessarily the same as the results for regression on Y. 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 straight line.
	Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.		Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.

	[[Image:Normal RRX Setting.png~~\|thumb~~\|center\|~~250px~~\| ]]		[[Image:Normal RRX Setting.png\|center\|550px\| ]]

	The plot of the solution for this example is shown next.		The plot of the solution for this example is shown next.

	[[Image:Normal RRX Plot.png~~\|thumb~~\|center\|~~250px~~\| ]]		[[Image:Normal RRX Plot.png\|center\|550px\| ]]
	<math></math>		<math></math>

Nicolette Young at 18:59, 25 April 2012

2012-04-25T18:59:54Z

← Older revision		Revision as of 18:59, 25 April 2012
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	Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.		Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.

	[[Image:Normal RRX Setting.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Normal RRX Setting.png\|thumb\|center\|250px\| ]]

	The plot of the solution for this example is shown next.		The plot of the solution for this example is shown next.

	[[Image:Normal RRX Plot.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Normal RRX Plot.png\|thumb\|center\|250px\| ]]
	<math></math>		<math></math>

Harry Guo at 23:35, 10 February 2012

2012-02-10T23:35:06Z

← Older revision		Revision as of 23:35, 10 February 2012
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	'''Solution'''		'''Solution'''

	~~Table 8.2~~ constructed in [[Normal distribution example 2\|Example 2]] applies to this example also. Using the values on this table, we get:		The table constructed in [[Normal distribution example 2\|Example 2]] applies to this example also. Using the values on this table, we get:

	::<math>\begin{align}		::<math>\begin{align}

Harry Guo at 21:04, 10 February 2012

2012-02-10T21:04:12Z

← Older revision		Revision as of 21:04, 10 February 2012
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	::<math>\begin{align}		::<math>\begin{align}
	\hat{b}= & \frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}{{y}_{i}}-\tfrac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}}{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,y_{i}^{2}-\tfrac{{{\left( \underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}} \right)}^{2}}}{14}} \\		\hat{b}= & \frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}{{y}_{i}}-\tfrac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}}{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,y_{i}^{2}-\tfrac{{{\left( \underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}} \right)}^{2}}}{14}} \\
	\widehat{b}= & \frac{365.2711-(630)(0)/14}{11.3646-{{(0)}^{2}}/14}=32.1411		\widehat{b}= & \frac{365.2711-(630)(0)/14}{11.3646-{{(0)}^{2}}/14}=32.1411
	\end{align}</math>		\end{align}</math>
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	and:		and:

	::<math>\hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}}{14}-\widehat{b}\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}</math>		::<math>\hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{t}_{i}}}{14}-\widehat{b}\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}</math>

	or:		or:

Harry Guo at 21:02, 10 February 2012

2012-02-10T21:02:58Z

← Older revision		Revision as of 21:02, 10 February 2012
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	Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.		Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.

	[[Image:~~weibullfolio1~~.png\|thumb\|center\|400px\| ]]		[[Image:Normal RRX Setting.png\|thumb\|center\|400px\| ]]

	The plot of the solution for this example is shown next.		The plot of the solution for this example is shown next.

	[[Image:~~weibullfolioplot1~~.png\|thumb\|center\|400px\| ]]		[[Image:Normal RRX Plot.png\|thumb\|center\|400px\| ]]
	<math></math>		<math></math>

Harry Guo at 18:54, 10 February 2012

2012-02-10T18:54:58Z

← Older revision		Revision as of 18:54, 10 February 2012
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	'''Normal Distribution RRX Example'''		'''Normal Distribution RRX Example'''

	Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.		Using the data of [[Normal distribution example 2\|Example 2]] and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.


	'''Solution'''		'''Solution'''

	Table 8.2 constructed in Example 2 applies to this example also. Using the values on this table, we get:		Table 8.2 constructed in [[Normal distribution example 2\|Example 2]] applies to this example also. Using the values on this table, we get:

	::<math>\begin{align}		::<math>\begin{align}

Harry Guo at 18:53, 10 February 2012

2012-02-10T18:53:53Z

← Older revision		Revision as of 18:53, 10 February 2012
Line 2:		Line 2:

	Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.		Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.


	'''Solution'''		'''Solution'''

Harry Guo: Created page with ''''Normal Distribution RRX Example''' Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, $\…'$

2012-02-10T18:53:43Z

Created page with ''''Normal Distribution RRX Example''' Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\…'

New page

'''Normal Distribution RRX Example'''

Using the data of Example 2 and assuming a normal distribution, estimate the parameters and determine the correlation coefficient, <math>\rho </math> , using rank regression on X.

'''Solution'''

Table 8.2 constructed in Example 2 applies to this example also. Using the values on this table, we get:

::<math>\begin{align}
\hat{b}= & \frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}{{y}_{i}}-\tfrac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}}{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,y_{i}^{2}-\tfrac{{{\left( \underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}} \right)}^{2}}}{14}} \\
\widehat{b}= & \frac{365.2711-(630)(0)/14}{11.3646-{{(0)}^{2}}/14}=32.1411
\end{align}</math>

and:

::<math>\hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{T}_{i}}}{14}-\widehat{b}\frac{\underset{i=1}{\overset{14}{\mathop{\sum }}}\,{{y}_{i}}}{14}</math>

or:

::<math>\widehat{a}=\frac{630}{14}-(32.1411)\frac{(0)}{14}=45</math>

Therefore:

::<math>\widehat{\sigma }=\widehat{b}=32.1411</math>

and:

::<math>\widehat{\mu }=\widehat{a}=45\text{ hours}</math>

The correlation coefficient is obtained as:

::<math>\widehat{\rho }=0.979</math>

Note that the results for regression on X are not necessarily the same as the results for regression on Y. 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 straight line.
Using Weibull++ , Rank Regression on X (RRX) can be selected from the Analysis page.

[[Image:weibullfolio1.png|thumb|center|400px| ]]

The plot of the solution for this example is shown next.

[[Image:weibullfolioplot1.png|thumb|center|400px| ]]
<math></math>