Week16-4up - 364 STA 2023 c D.Wackerly - Lecture 27 STA...

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Unformatted text preview: 364 STA 2023 c D.Wackerly - Lecture 27 STA 2023 c D.Wackerly - Lecture 27 365 STA 2023 Final Exam Locations Thought: The early bird may get the worm, but the Tuesday, 12/17/02, 10:00 am – 12:00 noon second mouse gets the cheese. Final Exam Sections £¡¡ §£¡¡ §& ! %¤¢¢©¢¢¡ &£¡¡ §¥¡¡ §#¡ %¤¢¨©¢¡ £¢('¢©"¤¢¡ ¡¡ §¡£¡¡ §£¡ #¡¡ §!¡¡ §!¡ ¢©¢¡ ¥# §¥¡¡ §&¡ $¨¢¢¢¡ ¡¡ § £¡¡ §#£¡ ¢¢%¤©"¤¢¡ #£¥# § ¡¡ §¡ %$¢©¢¡ "¤¢¢¢©¢¢¡ £¡¡ §¡¡ § ! ¢¢¢¡ ¡¡ §¡¡ §¡¡ ¡¡ §¡¡ §¥£¡ ¢¢©¨¦¤¢¡ Antara Roy Sourish Saha Mathew Smeltzer Kelly Sodec Michael Thomas TUR L007 Help Sessions for Final : CAR 100 This week, M, T, W, R, 3rd–8th per., FLO 104 NRN 137 Monday 12/16/02 NRN 137 – 3rd – 8th per., FLO 104 CLB C130 – 5:30 pm – 7:30 pm, NPB 1001 CAR 100 STA 2023 c D.Wackerly - Lecture 27 366 Last Time: STA 2023 c D.Wackerly - Lecture 27 How about the population of all possible could be observed when Probabilistic Model values that ? GED I(IC H 6 G E FD C A9 3 6 4 B@8753 1 20 deterministic part 367 1 YA Adam Meyers TUR L007 Wednesday : Optional question and answer session. ¥ Saurabh Kumar CLB C130 Tuesday : Exer. 11.47, 48, 49, 51, 55 W 50 Salvador Gezan CAR 100 Today : Pages 537 – 542 Donte Ford CAR 100 ) David Finlay Location ) Instructor Assignments : random error Assumptions: U SQ ¦TRH P each have a Normal distribution with mean 0 and standard deviation, V ) The errors, . ) The errors for different observations are INDEPENDENT. formula sheet S rr a "i©a `G E D P C I(IC ‘ ‰‡ ˆ† ” table standard errors E (D ` G E FD C 9p ‘ ‰‡ “† @3  1 XA values when formula sheet (p. 531) ’ UG 1 XA  W 50 ) W 50 ) W 50 9 @3  753 64 W 50 V is is CI for „ …ƒ The standard deviation of the ‚"€xyvws%ug5s tt  fe W caa d©b1 ` S values when estimator ca ga The mean of the values have a Normal distribution 1 ) The . hh a Fia where Implications: Consider the population of all possible values that could be observed when : p3 9 qW V points around the linear relationship. An unbiased estimator for hr a "ia describes the variability of data ` @V The “parameter”  1 YA ) 368 1 @¢4 93¡ versus STA 2023 c D.Wackerly - Lecture 27 369 Correlation : Section 11.6–7  Consider testing (p. 530) STA 2023 c D.Wackerly - Lecture 27 Example: Below are the scores for 20 student on the first exam in the course (%) and their overall total p-value ¨ £ ©‡ ¥ ¨ course score (in percent) U  ¦9 ¥ ¡ ¤ £ RR § ‡ ‰‡ P ‡ ¥ 1st Exam Course 1st Exam Course Score Total Score Total U ¨ £ ¨ ‡   ‡ § P ‰‡ W  ‡  ¦9  80 84 87 50 75 83 90 90 82 77 73 66 75 76 70 73 59 55 87 93 82 76 87 86 70 68 79    89 84 83 degrees of 3 ‡ 1 9  3 W    fe W r"ri©a a ! ” "S  $@3 W 9p ) 1‡  1‡ W‡ STA 2023 c D.Wackerly - Lecture 27 370  distribution with 99 62 NULL HYPOTHESIS 99 91 ` ‰ ¥‡ `‘¨R‡ ‘ ‰ ‡ W standard error 76 100 hypothesized value freedom. 76 79 Formula Sheet has a   estimator (tail area) # TEST STATISTIC or 70 # 78 # OR # 3 OR STA 2023 c D.Wackerly - Lecture 27 371 Exam Score Data: 1 `% 0 ¡&§ # RI£ $ 1 `% A ¥¥#§¥ ¢B¨"£ # ! A # ’  6  ’  hh a ¡!§ ¢R 1 Fi©a $ '(¢¢B£ 1 &&§ !#§ # ¢¢B"£ 1 p0 & § ¢ £ 1 % 0% A % &A 1 ¥§ B¢£ $ 1 % 0 $ $ ! ’  # # ’  1 @3 1 53 4p 9p hr a "i©a ( ’ (B! rr a '  ¡ £  § 1 "ia Cement Data: Regression Analysis The regression equation is Final = 29.5 + 0.627 Exam1 Predictor Constant Exam1 Coef 29.53 0.6265 StDev 10.00 0.1252 S = 6.874 R-sq = 58.2% T 2.95 5.00 P 0.009 0.000 R-Sq(adj) = 55.9% Analysis of Variance Source Regression Error Total DF 1 18 19 SS 1183.5 850.5 2034.0 MS 1183.5 47.2 F 25.05 P 0.000 Seems to be a “stronger” relationship in the cement data than in the grades data. How can I quantify this?? 372 STA 2023 c D.Wackerly - Lecture 27 STA 2023 c D.Wackerly - Lecture 27 373 Correlation measures the strength and there is a strong linear ) relationship with negative slope. ¤) one or both variables will not alter . Ex. ha Fh a rr a "i©a can be measured in inches, feet, yards, meters, etc. and stays the same. hFh a©a "r a ra hr a "i©a ¤) 1 ¡ £ the SIGN (pos. or neg.) of there is a PERFECT linear relationship ¢ ££ ¢ £6 W) 1 ) with positive slope. 9p @3 1 ) The SIGN (positive or negative) of . the value of 9 p3 Properties of : is unitless – changing the unit of measurement for How is it measured? – The Correlation Coefficient, . A variables. If is close to £W If usefulness of the linear relationship between two is the same as measures the strength of the LINEAR relationship between two variables. It may or may not detect NONLINEAR associations. is close to £6 ) If there is a strong linear relationship with positive slope. £W 1 If there is a PERFECT linear relationship ) with negative slope. ! ¢# ¥ ’ 1 Grades on Exam1 versus Final, 374 STA 2023 c D.Wackerly - Lecture 27 STA 2023 c D.Wackerly - Lecture 27 375 ¡& ¢ ’ W 377 Coefficient of Determination, The sign of 1 Cement: Strength vs. water/cement ratio, STA 2023 c D.Wackerly - Lecture 27 ¡ ¢ 376 STA 2023 c D.Wackerly - Lecture 27 , Sec. 11.7 tells whether the fitted line has a positive or negative slope. also contains useful 1` ¤©¤ ©a "r a ara ha "` r ©a £ §¨¤¦¤¥a©"5a arra ” ha "r ©a 1` W 50 ` ¤) A ¢ ’  # total variability among the ` U % A 9 p 3 6 4 p 3 P  W W 50 % 0P  1 ¡& ¢ ’ W ) W 50 ha Fh ©a 0   1 is the variability of the 1 ¡!  ’  1 ' rr a "i©a  ’  ¤ ’  #  ¡! ” ¥ ¨¡  ’  W 1 ¥ ¨¡  ’  W hFh a©a "r a ra hra I5a 1 hr a "ia 1 ¡ ) ca d©a ca d©a ) explained by fitting the line. ! # ¥ ’ 1 Example: Exam score data: 1 &  ’ 1` Interpretation : of the variability among final course scores can be explained by a linear function of the first exam score. # 1 1` Interpretation : &# ¢ ’ Example: Cement data: P 0.009 0.000 R-Sq(adj) = 55.9% R-sq = 58.2% 1 S = 6.874 T 2.95 5.00 ¡&  ’ W  ’  & Regression Analysis The regression equation is Final = 29.5 + 0.627 Exam1 Predictor Coef StDev Constant 29.53 10.00 Exam1 0.6265 0.1252 of the variability in can be explained by a Regression Analysis The regression equation is Strength = 2.56 - 1.05 W/C rat Predictor Chef StDev Constant 2.5606 0.1400 W/C rat -1.05439 0.09527 T 18.28 -11.07 S = 0.04608 R-Sq(adj) = 96.0% R-sq = 96.8% P 0.000 0.000 quantifies the values around the fitted line. W 50 % ' hh a (5a variability of the 1 ` '0 W U 1 values 378 1 values that is explained by the linear function of . Example: Grades on Exam1 vs. Final (See page 371) STA 2023 c D.Wackerly - Lecture 27 hFh a©a ha Fh ©a represents the fraction of the variability among the W is called the Coefficient of Determination. Example: Cement (See pages 368-59) values that is NOT a ©a information. The magnitude (size) of ...
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This note was uploaded on 07/28/2011 for the course STA 2023 taught by Professor Ripol during the Fall '08 term at University of Florida.

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