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Prob & Statistics Engineering

by: Aryanna Jerde

Prob & Statistics Engineering STT 351

Aryanna Jerde
GPA 3.72

Raoul Lepage

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Raoul Lepage
Class Notes
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This 2 page Class Notes was uploaded by Aryanna Jerde on Saturday September 19, 2015. The Class Notes belongs to STT 351 at Michigan State University taught by Raoul Lepage in Fall. Since its upload, it has received 21 views. For similar materials see /class/207817/stt-351-michigan-state-university in Statistics and Probability at Michigan State University.


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Date Created: 09/19/15
LittleSo ware4nb 1 Example of multiple linear regression and exercises due 111207 Example 1 Data is gathered on 7 taxable properties Here are the scores observed for independent variables and dependent variable y 9611 tax pa1d last year 16121 busmess 0 1f not y aud1t determmed tax due th1s year 2300 0 3000 7200 0 7800 1200 0 1321 4700 0 5100 1900 0 2200 5300 1 5800 1a Determine the least squares coefficients ofafit of the model yi o 1 31x11 132 x12 5 In55 xtax 1 2300 0 1 7200 0 1 1200 0 1 4700 0 1 1900 0 1 5300 1 Out55 1 2300 o 1 7200 o 1 1200 o 1 4700 o 1 1900 o 1 5300 1 In56 ytax 3000 7800 1321 5100 2200 5800 muss 3000 7800 1321 5100 2200 5800 In57 betahattax betahat xtax ytax 1 0 Out57 255027 10485 l36328 1b From the above 3 256027 10486 7136328 Calculate the anticipated auditidetermined tax for the average property if M1 3900 is the population average tax for all properties in the community M2 018 is the fraction of properties in the community that are businesses Note this is in fact the regressionibased estimate of My It is computed as the dot product of 1 3900 018 with In58 betahattax1 3900 013 muss 434313 1c So based on a withereplacement sample of the above siX properties the regressionibased estimator of My is 434313 dollars In order to use this estimate we had to know the population means 3900 and 018 as above If the community has 2000 properties we would estimate from this that the total auditidetermined value of all 2000 properties is around 2000 times 434313 Sample size n 6 is not a large enough but just to illustrate had n been large we39d have been entitled to margin of error 1 96 1 R2 ly 39 Fn which would better the margin of error without the term V 1 R2 applicable to just using y What is the multiple correla7 tion R for this admittedly small sample of only six In59 Rxtax ytax10 Out59 0997381 From R 0997381 above we find V 1 R 00723266 indicating that this model appears to be doing a fine job of improve ing upon the estimate of My It is little over 7 of the width of the Cl based onjust y LittleSo ware4nb 2 In60 Sqrt1 0997381A2 Out60 00723255 1d Based on our fit to six sample properties what does the model estimate for the auditidetermined tax of a business property whose tax last year was 5900 Just feed the properties Xiscores 1 5900 1 into the fitted model ie take the dot product 35 5900 1 In53 betahattax 1 5900 1 Out53 542915 Had the property been nonibusiness our fitted model would anticipate an auditidetermined tax of 64428 In61 betahattax1 5900 0 01mm 64428 1e Findthe residuals y1 x ofthe fit In54 residxtax ytax 10 Out54 332182 598189 193353 844599 483755 0 1f According to the fitted model what is the increase in projected auditidetermined tax for every 1000 increase in tax paid last year ans The coefficient of tax paid last year is 31 10486 so the anticipated increase is 104860 7 1000 4860 dollars The following are due Monday 111207 Exercises from chapter 11 1 26 28 30 32 2 Use routines from Little Software4 to determine betahat residuals and R from example 1112 Compare your results with those reported on page 526 3 For exercise 35 pg535 verify the reported betahat using Lttle Software4 don39t submit the problem itself 4 Exercise 38 pg 537 and verify the repoted R2 and fitted values 9 XfS using Little Sortware4 Below I39ve worked out R2 3 and y X for observations one through seven only In24 y38 7 63 013 049 7 1 04 0065 Out24 07 053 0013 0049 07 01 004 00055 In30 MatrixFormy38 Out 30Ma trixForm 7 063 013


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