Week16-2up - Instructor David Finlay Michael Thomas Kelly...

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Unformatted text preview: Instructor David Finlay Michael Thomas Kelly Sodec Mathew Smeltzer Sourish Saha Antara Roy Adam Meyers Saurabh Kumar Salvador Gezan ¦¡¡ ¦¡¡ ¢¡¡ ¢£ ¡ ¦£ ¦¡¡ ¡ ¡ ¢¡¡ Donte Ford Sections ¡ ¡¡ ¢¡¡ ¡¡ ¡¡ ¢¡¡ ¡¡ ¡ ¡¡ ¢¡¡ ¤ © ¤ § ¤ ¦ ¤ § ¤ § ¤  ¤ §¦ ¤ ©© ¤ §¡ ¥£ ¤ ¡¡ ¡¡ ¢¡¡ ¦¡¡ ¦¡¡ ¢¡¡ ¡¡ ¡¡ ¡¡ ¦¡¡ ¤ §¢ ¤ §£ ¤ ¡ ¤  ¥£ ¤ © ¤ ©§ ¤ §§ ¤ ¨§ ¤ § ¤ 364 CAR 100 CLB C130 NRN 137 NRN 137 CAR 100 TUR L007 TUR L007 CLB C130 CAR 100 CAR 100 Location Final Exam Tuesday, 12/17/02, 10:00 am – 12:00 noon STA 2023 Final Exam Locations STA 2023 c D.Wackerly - Lecture 27 ¨ © ¨  ¦¦¡ §  ¢¦¡ ¢¡ § Monday 12/16/02 – 5:30 pm – 7:30 pm, NPB 1001 – 3rd – 8th per., FLO 104 This week, M, T, W, R, 3rd–8th per., FLO 104 Help Sessions for Final : Wednesday : Optional question and answer session. Tuesday : Exer. 11.47, 48, 49, 51, 55 Today : Pages 537 – 542 Assignments : second mouse gets the cheese. Thought: The early bird may get the worm, but the STA 2023 c D.Wackerly - Lecture 27   365 describes the variability of data The values when values have a Normal distribution The mean of the ¡ § The standard deviation of the £ ¤¢   ¥ ¨  values that could be observed when ¦¢ is ¨    Implications: Consider the population of all possible points around the linear relationship. The “parameter” INDEPENDENT. The errors for different observations are . each have a Normal distribution random error with mean 0 and standard deviation, The errors,  ¡ Assumptions:  ¨ ¤¢ £ deterministic part    © ¥ ¦ ¤¢ §  ¥  values when is . where An unbiased estimator for could be observed when !  Probabilistic Model ¡ ¨ ©  § " )0  ¨ #"  $¦ 0 estimator ¨ 1 )  § ¡ 2 formula sheet  : ? CI for table 367 values that (p. 531) %&"  How about the population of all possible @9 © 34 ¦ ¤¢ ' 5 B    standard errors formula sheet  "D ¡ § !  " ! A % STA 2023 c D.Wackerly - Lecture 27 " £ ¡ #" @9 ¨ © A B ! ¨ ¡ 7 86 ( &" ¨  " © ( ¦ ¢' C  Last Time: 366 ( &" STA 2023 c D.Wackerly - Lecture 27 % Formula Sheet has a RR estimator TEST STATISTIC ¦ ¤¢ OR ¦ ¤¢ OR © versus Consider testing (p. 530) ¦ ¤¢ ¢£ ¡ ¤ § § § freedom. or p-value  STA 2023 c D.Wackerly - Lecture 27   @   @ © @ ¤@ ¡ @ ©  (tail area) hypothesized value distribution with 368 degrees of NULL HYPOTHESIS standard error ¡ ¡ @  ¦ ¤¢ '  @ ¤@ @ B A A  @   "D  @ ¡ £  ¦ ¤¢ ¦ A A ! B ! ¡ @¥ @¥  ( &" Course 1st Exam Course 1st Exam course score (in percent) first exam in the course (%) and their overall total Example: Below are the scores for 20 student on the Correlation : Section 11.6–7 STA 2023 c D.Wackerly - Lecture 27 Total 87 83 84 100 79 73 66 79 89 86 87 87 93 70 62 82 76 78 91 70 Score 84 70 82 59 75 77 90 50 99 76 Score 83 68 76 55 76 73 90 75 99 80 Total  § ¦ §© @  § ( $¦  ¦ §¤ @ ¢¦ ¢¦  ¨  ¨   369 Source Regression Error Total DF 1 18 19 Analysis of Variance SS 1183.5 850.5 2034.0 R-sq = 58.2% S = 6.874 P 0.009 0.000 F 25.05 P 0.000 R-Sq(adj) = 55.9% T 2.95 5.00 MS 1183.5 47.2 StDev 10.00 0.1252 Coef 29.53 0.6265 Predictor Constant Exam1 The regression equation is Final = 29.5 + 0.627 Exam1 Regression Analysis 370 Exam Score Data: STA 2023 c D.Wackerly - Lecture 27 " How can I quantify this?? data than in the grades data. Seems to be a “stronger” relationship in the cement Cement Data: ¦ ¤¢ ' STA 2023 c D.Wackerly - Lecture 27 ¨ ( &" ( ¨ § ¡ § ¦ C §¢ ¡ C ¡ ¤¢ ¡ ¤¢ ¨© £ ¤¢ ' ¡ ¨ ¦ ¡ ¡ ¤ ©£ § § " ( &" %   ' ¦¢ © §! ! ¤ ¡ ¤¢ ¡ ¦ ¡ ¡ § © ¨ C " © ¡ § ¦¢ ¡¢ ¦ ¤ ¥£  ¤  % &" % ¨ C ¦ ¥ 371 § ¨ ¨¡ ££ ¡ ¤¦ C ¡ § Properties of : % " ¡ is close to there is a strong linear there is a PERFECT linear relationship with negative slope. If relationship with positive slope. If % there is a PERFECT linear relationship with positive slope. If ¡ ¦ ¢' How is it measured? – The Correlation Coefficient, . variables. usefulness of the linear relationship between two    " " 372 is close to there is a strong linear 373 can be stays the same. . is the same as NONLINEAR associations. between two variables. It may or may not detect measures the strength of the LINEAR relationship the SIGN (pos. or neg.) of The SIGN (positive or negative) of the value of measured in inches, feet, yards, meters, etc. and one or both variables will not alter . Ex. is unitless – changing the unit of measurement for relationship with negative slope. If STA 2023 c D.Wackerly - Lecture 27 Correlation measures the strength and (" % &"  STA 2023 c D.Wackerly - Lecture 27 % &" " ¡  ( &" ( &" " ¢  ¢ ¡ ¢ ¡ ¥¢ ¢ ¢ ( % ¢  ( ¥¢ ¦ ¢'    § Grades on Exam1 versus Final, ¡ C STA 2023 c D.Wackerly - Lecture 27 £ 374 STA 2023 c D.Wackerly - Lecture 27 375 " " ( (" " % ¡ © ¡ C 376 The magnitude (size) of information. , Sec. 11.7 also contains useful of . values variability of the explained by fitting the line. is the variability of the values that is NOT values around the fitted line. quantifies the total variability among the values that is explained by the linear function represents the fraction of the variability among is called the Coefficient of Determination. the 377 tells whether the fitted line has a positive or negative slope. The sign of Coefficient of Determination, STA 2023 c D.Wackerly - Lecture 27 ! © ¦§ ¡ ¡ ¡ ¡ Example: Grades on Exam1 vs. Final (See page 371) ¡ Example: Cement (See pages 368-59) (" " Cement: Strength vs. water/cement ratio, ( &" ( &" " % C ¦§ ¡£ % &" " (  C ¦§ D  ¡  ¡ % § C ¦§ ¡£ ¦§ C ¡ C ¦ ¡ ¡ ¡     %&"  ¢ "  ¡ ! % &" " © ( ¦  § % #" #" " "  ¦§ ¡ ( &" ( &" ¡ %" % £ ¤" % £    C ¡ ¡ ¡ £ £ ¤" ! ¥ !   £ ¤¢ ' © " ( &" C " ! ¡ ( ¥ ¦¤¢ ' §  " % " % &" " "D ¡ " (" %! ¨ " % STA 2023 c D.Wackerly - Lecture 27 " R-sq = 58.2% Example: Cement data: S = 6.874 R-Sq(adj) = 96.0% R-sq = 96.8% S = 0.04608 P 0.000 0.000 T 18.28 -11.07 can be of the variability in 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 explained by a Interpretation : P 0.009 0.000 R-Sq(adj) = 55.9% 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 ! ¡ C © ¡ ¡ C C ¡ T 2.95 5.00 Interpretation : of the variability among final course scores can be explained by a linear function of the first exam score. Example: Exam score data: ! ¡ C STA 2023 c D.Wackerly - Lecture 27 ¡ C ¡ ¨ ¦  £ ¦¨ © 378 ...
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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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