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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
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¢¢©¨¦¤¢¡ 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
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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
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
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 pvalue ¨ £ © ¥
¨ 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 ¥¥#§¥
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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 Rsq = 58.2% T
2.95
5.00 P
0.009
0.000 RSq(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 RSq(adj) = 55.9% Rsq = 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 RSq(adj) = 96.0% Rsq = 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 36859) 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.
 Fall '08
 Ripol
 Statistics

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