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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STA 2023 c D.Wackerly - Lecture 27 364 STA 2023 Final Exam Locations Tuesday, 12/17/02, 10:00 am – 12:00 noon Final Exam Salvador Gezan Saurabh Kumar Adam Meyers Antara Roy Sourish Saha Mathew Smeltzer Kelly Sodec Michael Thomas CAR 100 §0!" #¢¢¡ §'¡ ¢¢¡ §©£¡ &1$¡ §"¡ #¢¢¡ §¢¡ 0¡ §'£¡ #(¤¢¡ §©¡ &¢¡ §!!" #¢¢¡ §¤¢¡ ¡¡ §¥£¡ ¨¦¤¢¡ Donte Ford Location §£¡ 4¢¡ §3¥ ¡ ¡ §¡£¡ ¤2¤¢¡ §"©¡ ¢¡ §¨¡ ¥©¡ §!£¡ )$¢¡ §!¡ ¢¡ §¡ ¢¢¡ §¡ ¡ §©¡ ¢¡ David Finlay Sections £¡ )$¡ 0£¡ (¤¢¡ £¡ ©¡ '©¡ ¡ ©¥ ' ©¢¡ ©¡ '£ (&¥ ' £¡ %$¡ !¡ © ¢¡ ©¡ ¢¡ Instructor CAR 100 CLB C130 TUR L007 TUR L007 CAR 100 NRN 137 NRN 137 CLB C130 CAR 100 STA 2023 c D.Wackerly - Lecture 27 Thought: The early bird may get the worm, but the second mouse gets the cheese. Assignments : Today : Pages 537 – 542 Tuesday : Exer. 11.47, 48, 49, 51, 55 Wednesday : Optional question and answer session. Help Sessions for Final : This week, M, T, W, R, 3rd–8th per., FLO 104 Monday 12/16/02 – 3rd – 8th per., FLO 104 – 5:30 pm – 7:30 pm, NPB 1001 365 STA 2023 c D.Wackerly - Lecture 27 366 Last Time: Probabilistic Model   © ¥   ©  § ¨¦ ¢ ¥ ¤¢ £ ¡ deterministic part random error Assumptions: " #!  each have a Normal distribution with mean 0 and standard deviation, $ The errors, . The errors for different observations are INDEPENDENT. describes the variability of data $ The “parameter” points around the linear relationship. Implications: Consider the population of all possible ¡§ . values have a Normal distribution values when ¦ ¢  ¥ ¤¢ £ $ is % ¤ % ¤ The standard deviation of the ¡§ % ¤ The mean of the  % ¤ The  values that could be observed when is values when  ¡§ STA 2023 c D.Wackerly - Lecture 27 367 ¡§ : CI for (p. 531) & " standard errors     © ##© %#! $" table formula sheet %" ! $ ¨¨ ('¡ ¡    © formula sheet ?        ©%£ ¡ ¢¡¡ where estimator values that ¤¨ ©¥¡ ¡ ¦ § ¢ % ¦¥¡ ¡ ¡ ¢ ¡ ¡ ¤¤ $ An unbiased estimator for ¥ could be observed when % How about the population of all possible ¦ §¢ STA 2023 c D.Wackerly - Lecture 27 368 ¡ p-value £ © ! " ¥ ¨¢ ¥ § ! "! ¤  ! ! £ ¦¢ £  OR ¥ ¨¢ ¦! §¥ ¢ ¡ RR " £ versus  ¡¦¢ Consider testing (p. 530) "! %  ¤ © ! ©  ¦¢ OR (tail area)  © or $%" ! £ ! %" ! % $ © !  ¡ ¦¢ TEST STATISTIC hypothesized value  ¡!   ©%£   %! freedom. distribution with ¨¨ ('¡ ¡ ¡! has a NULL HYPOTHESIS  % ¦ §¢ Formula Sheet  % standard error   estimator degrees of  STA 2023 c D.Wackerly - Lecture 27 369 Correlation : Section 11.6–7 Example: Below are the scores for 20 student on the first exam in the course (%) and their overall total course score (in percent) 1st Exam Course Course 1st Exam Score Total Score Total 78 70 76 80 84 76 99 99 100 87 50 75 79 83 90 90 91 82 77 73 62 66 75 76 70 73 59 55 87 93 82 76 87 86 70 68 79 89 84 83 STA 2023 c D.Wackerly - Lecture 27 370 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 How can I quantify this?? data than in the grades data. Seems to be a “stronger” relationship in the cement Cement Data: '© " "!  & © ¡ £ § ¢ '© ' &  ¡ ¦ § ¢ § ' &  ¥  & !© ¡ § ¡¢ §© " ¡0 ¡ ¡£ § ¡ ¦¤¥¡ ¡ £!¢0 § ¡ ¤(¨¥¡ ¡ ¢! & 24 #" ¡ ('¡ ¡ ¤ ¨¨ ¡ § " §'© ¢¢' #1£ ¡ 0 #1£  §'© ¡ ¥' §3¥©1£ ¥ ¡ § 0 § ¢ £ !  £ ¥§ ¡ ¡ § Exam Score Data: STA 2023 c D.Wackerly - Lecture 27 371 STA 2023 c D.Wackerly - Lecture 27 372 Correlation measures the strength and usefulness of the linear relationship between two variables. How is it measured? – The Correlation Coefficient, . ¤¦¥¡ ¡ ¤ ¨¨ (¥¡ ¡ ¤ ¨¨ ¦ § ¢ ¡ ¤¦¥¡ ¡ ('¡ ¡ ¤¨ ('¡ ¡ ¡ Properties of : ¡ £% ¡ £ £¥ ¡ If there is a PERFECT linear relationship with positive slope. is close to £¥ If there is a strong linear relationship with positive slope. £% ¡ If there is a PERFECT linear relationship with negative slope. STA 2023 c D.Wackerly - Lecture 27 is close to £% If 373 there is a strong linear relationship with negative slope. is unitless – changing the unit of measurement for § one or both variables will not alter . Ex. can be measured in inches, feet, yards, meters, etc. and stays the same. The SIGN (positive or negative) of ¦ §¢ the SIGN (pos. or neg.) of the value of is the same as . measures the strength of the LINEAR relationship between two variables. It may or may not detect NONLINEAR associations. STA 2023 c D.Wackerly - Lecture 27 " ¢' ¥ & ¡ Grades on Exam1 versus Final, 374 STA 2023 c D.Wackerly - Lecture 27 375 STA 2023 c D.Wackerly - Lecture 27 376 ¡0 ¢! & % ¡ Cement: Strength vs. water/cement ratio, Example: Cement (See pages 368-59) !¢'© &  ¡ ¦¤ ¡ ¡ ¤ ¡0 ¢! & % ¡ ¥ ¡ ©&  % ¡ ¡"© &  ¡ (¨ ¡ ¡ ¨ !' ¢© &   ¡" © &  ¤¤ ¨¨ ¡ ¦¥¡ ¡ ('¡ ¡ ¡ ¤(¨'¡ ¡ ¡ ¥ ¡ ©&  % ¡ (¨ ¡ ¡ ¤ Example: Grades on Exam1 vs. Final (See page 371) STA 2023 c D.Wackerly - Lecture 27 377 The sign of ¡ ¢ Coefficient of Determination, , Sec. 11.7 tells whether the fitted line has a positive or negative slope. The magnitude (size) of also contains useful information. ¤¤ ¦'¡ ¡ £ ¨¨ ¡ £ ¥¡ ¡ ('¡ ¡ ¡ ¤ ¤ © ¨ ¡ ¡ ¡ ¡ % ¦¤ ¡ ¡ £ £¤¡ ¡ ('¡ ¡ ¨¨ ¤ (¨ ¡ ¡ ¡ is called the Coefficient of Determination. % the represents the fraction of the variability among values that is explained by the linear function ¡ ¢¡¡ % ¤ ¡ ¤¦¤'¡ ¡ § of . ¡ " %  % ¤  § ¨" § ¦ § ¢ ¥ £ § ¢ % ¦ variability of the quantifies the values around the fitted line. is the variability of the ¢¡¡ explained by fitting the line. % ¤ values total variability among the values that is NOT STA 2023 c D.Wackerly - Lecture 27 378 " ' ¥ & ¡ Example: Exam score data: ¡ ©0 & ¡ Interpretation : of the variability among final course scores can be explained by a linear function of the first exam score. © &  0 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 0'¢! & ¡ ¡ Interpretation : Example: Cement data: R-Sq(adj) = 55.9% ¡ R-sq = 58.2% P 0.009 0.000 ¡0 ! & % S = 6.874 T 2.95 5.00 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 ...
View Full Document

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.

Ask a homework question - tutors are online