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![Page 1: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/1.jpg)
Last time:Last time:
One-way Analysis of VarianceOne-way Analysis of Variance
![Page 2: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/2.jpg)
Example• List of 50 spoken words• 3 x 10 Subjects (split among I=3 groups)• Group 1: (Fast sound) Person in movie reads list, but
sounds precede lip movement slightly• Group 2: (Slow sound) Person in movie reads list, but
sounds lag behind lip movement slightly• Group 3: (Synchrony) Person in movie reads list with
auditory and visual stimuli in synchrony• Memory Task: Subjects are asked to recall as many
items as possible.
![Page 3: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/3.jpg)
One-way Analysis of Variance Model Assumptions:
,1N ,2N ,iN ,IN
11
12
11
...
nX
X
X
22
22
21
...
nX
X
X
iin
i
i
X
X
X
...2
1
IIn
I
I
X
X
X
...2
1
I many Independent Groups
Data … …
Population
Sample Size1n
2n i
nIn… …
![Page 4: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/4.jpg)
One-way Analysis of Variance
,~ iij NX
,0~ , NX ijijiij
IH ...: 210
oneleast at :aH
![Page 5: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/5.jpg)
Similar recipe as in Linear Regression!
i
iiji
iijii
ij XXnXXXX22
,,
2
Sum SquaresTotal(SST)
Sum SquaresError(SSE)
Sum SquaresGroups(SSG)
Degrees of Freedom
DFT = N-1
Degrees of Freedom
DFG = I-1
Degrees of Freedom
DFE=N-I= +
1,,
1
:SquaresMean
I
SSGMSG
IN
SSEMSE
N
SSTMST
MSG
![Page 6: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/6.jpg)
IH ...: 210 2
2
,MSE pji
iij
SIN
XX
2 ofestimator unbiasedan is MSE
wellas ofestimator
unbiasedan isMSG 2
1 toclose be totends0 MSE
MSGH
INIFMSE
MSGH ,1~:0
![Page 7: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/7.jpg)
ANOVASource of Variation SS df MS F P-value
Between Groups 233.8667 2 116.9333 5.894698 0.007513Within Groups 535.6 27 19.83704
Total 769.4667 29
Let’s grind it out for our example…
MSG
89.583704.19
9333.116
MSE
MSG
Large MSG leads tosignificant F statistic.
Reject Null Hypothesis!Conclusion: The population means
are not identical across groups
![Page 8: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/8.jpg)
What if I=2?
2,1~ :Then NFMSE
MSG
Remember: The Square of a t Random Variable with
n-2 degrees of freedom is an F Random Variablewith 1 degree of freedom in the numerator and
with n-2 degrees of freedom in the denominator.
Thus, the one-way analysis of variance is a natural extensionof the comparison of two means from independent samples(with equal population variances).
![Page 9: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/9.jpg)
Robustness
• If the samples sizes are equal, then the assumption of equal variance (equal standard deviation) is not crucial.
• CLT helps with violations of normality, i.e. as long as sample sizes are large, we do not need normality of the X variables.
![Page 10: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/10.jpg)
Today:Today:
Wrap up “Loose Ends”Wrap up “Loose Ends”
An Illustrating Example An Illustrating Example on Simple Regressionon Simple Regression
Typo CorrectionTypo Correction
One last quiz…One last quiz…
![Page 11: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/11.jpg)
San Fernando Valley Real Estate Data
RENT FEET YRS DIST OFFICE POWER CLEAR LOAD PARK LOT SPRINK1 0.65 11000 0 12 1000 200 20 0 15 1.52 12 0.47 16544 0 12 2156 400 20 1 33 1.5 13 0.48 15004 0 12 2178 400 20 1 30 1.5 14 0.45 27960 1 16 5824 800 18 0 56 1.43 15 0.55 10665 1 13 1000 400 18 0 27 1.5 16 0.51 13700 1 7 1370 600 24 0 28 1.63 0
47 0.47 13440 23 20 2885 1600 14.5 0 17 1.79 048 0.56 14703 24 3 5500 1800 16 1 46 2.31 149 0.53 10000 30 9 800 200 14 1 30 3.19 050 0.5 10320 31 4 1000 400 14 0 22 1.84 151 0.58 27600 33 3 7600 2000 16 0 52 4.5 152 0.36 10360 33 20 730 200 12 0 0 0.8 0
etc.
![Page 12: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/12.jpg)
San Fernando Valley Real Estate Data
RENT FEET YRS DIST OFFICE POWER CLEAR LOAD PARK LOT SPRINK1 0.65 11000 0 12 1000 200 20 0 15 1.52 12 0.47 16544 0 12 2156 400 20 1 33 1.5 13 0.48 15004 0 12 2178 400 20 1 30 1.5 14 0.45 27960 1 16 5824 800 18 0 56 1.43 15 0.55 10665 1 13 1000 400 18 0 27 1.5 16 0.51 13700 1 7 1370 600 24 0 28 1.63 0
47 0.47 13440 23 20 2885 1600 14.5 0 17 1.79 048 0.56 14703 24 3 5500 1800 16 1 46 2.31 149 0.53 10000 30 9 800 200 14 1 30 3.19 050 0.5 10320 31 4 1000 400 14 0 22 1.84 151 0.58 27600 33 3 7600 2000 16 0 52 4.5 152 0.36 10360 33 20 730 200 12 0 0 0.8 0
(Rent per square foot)
(Square-footage)
![Page 13: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/13.jpg)
0
5000
10000
15000
20000
25000
30000
35000
0 10000 20000 30000 40000 50000 60000 70000
Sq. Feet
![Page 14: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/14.jpg)
Is there significant evidence for a linear relationship?
• Test using the correlation• Test using the slope• Test using the ANOVA table
![Page 15: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/15.jpg)
Dependent Variable: TotalRent Realest.xlsIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
Analysis of VarianceSource df Sum Sqrs Mean Sqr F P-value
Regression 1 1.67E+09 1.67E+09 410.179 0.000Residual 50 2.03E+08 4.07E+06
Total 51 1.87E+09
Y
Sample correlation R
n n-2t-stat
![Page 16: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/16.jpg)
Y
Sample correlation R
t-stat
0:
0:0
XYA
XY
H
H
2,22022
21
:if Reject ~
21
:Test
nn t
nR
rHt
nr
r
Dependent Variable: TotalRent Realest.xlsIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
![Page 17: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/17.jpg)
Y
Sample correlation R
t-stat
0:
0:0
XYA
XY
H
H
2,2222009.2253.20
2)944(.1
944.have We~
21
:Test
nn t
n
t
nr
r
Dependent Variable: TotalRent Realest.xlsIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
The correlation is significant at 5% significance level.Yes, significant evidence for a linear relationship.
![Page 18: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/18.jpg)
Dependent Variable: TotalRentIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
0:
0:0
iA
i
H
H
0̂
1̂0̂SE
1̂SE
Observedt-statistics for
*
* iSEi
ˆ
0ˆ p-value =
observedn ttP 2
toingcorrespond
95% CIs
![Page 19: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/19.jpg)
0:
0:
1
10
AH
H
1̂ 1̂SE
Observedt-statistic for
*
* 1ˆ
1 0ˆ
SE
p-value <.001Yes, significant evidence forlinear relationship
95% CI
Dependent Variable: TotalRentIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
![Page 20: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/20.jpg)
p-value <.001Yes, significant evidence forlinear relationship
Analysis of VarianceSource df Sum Sqrs Mean Sqr F P-value
Regression 1 1.67E+09 1.67E+09 410.179 0.000Residual 50 2.03E+08 4.07E+06
Total 51 1.87E+09
179.4100607.4
0967.1
E
E
MSE
MSM
![Page 21: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/21.jpg)
What is the best fitting regression equation?
![Page 22: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/22.jpg)
0̂
1̂
Dependent Variable: TotalRentIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
Feet Square 451.779.960Rent
![Page 23: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/23.jpg)
“I bet the population intercept is more then 900”
This would mean that you pay a fixed
minimum flat amount of $900,
plus whatever rent you need to pay
based on square footage.
![Page 24: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/24.jpg)
Dependent Variable: TotalRentIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
claim. for the evidencet significan No
009.211.951.521
900779.960
025.
900Intercept :
,900Intercept :0
AH
H
![Page 25: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/25.jpg)
I bet, for every additional 10 Square Feet,
you have to pay more than an extra $4 Rent!
That would mean more than $.4 extra rent per extra square foot.
That would mean the slope is > .4.
![Page 26: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/26.jpg)
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
50,02.1 109.2318.2
022.
4.451.4.
:statistic edstandardiz Observe
1
tSE
b
b
4.:4.: 1110 HH
Significant at 2% significance level.Yes, significant evidence that we pay over $4 extra per 10sqft extra.
![Page 27: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/27.jpg)
For every additional 1,000 Square Feet, how much extra Rent do you have to pay?
Give a 95% Confidence Interval
![Page 28: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/28.jpg)
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
]496,.407[.022.009.2451. :obtain wecase,our In
:slope for the Interval Confidence 95%
2
*2,21
XX
stb
i
n
This is our 95% CI for the extra Rent per extra Square Foot.Thus:95% CI for extra Rent per 1,000 Square Feet: [$407, $496]
![Page 29: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/29.jpg)
What is our best guess at the standard deviation of
the Error Term?
What percentage of the variance are we able to explain with this
model?
![Page 30: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/30.jpg)
22
n
SSEs
SST
SSR
SST
SSER 12
2n
SSEs
SSR = SST-SSE
n
i iYY YYSSST1
2)(
)ˆˆˆ()ˆ( 101
2 XYYYSSEn
i i
Dependent Variable: TotalRentIndependent Variables: SquareFeet
Descriptive StatisticsVariable Mean Std.Dev. Std.Err. Maximum Minimum Count
SquareFeet 1.98E+04 1.27E+04 1757.569 64570 5200 52TotalRent 9885.505 6059.211 840.261 32285 3016 52
Correlation MatrixVariable SquareFeet TotalRent
SquareFeet 1.000TotalRent 0.944 1.000
Regression StatisticsR R Square Adj.RSqr Std.Err. # Cases #Missing Deg.Free t(2.5%,50)
0.944 0.891 0.889 2017.147 52 0 50 2.009
Summary TableVariable Coeff. Std.Err. t Stat. P-value Lower95% Upper95%
Intercept 960.779 521.951 1.841 0.072 -87.591 2009.149SquareFeet 0.451 0.022 20.253 0.000 0.407 0.496
Analysis of VarianceSource df Sum Sqrs Mean Sqr F P-value
Regression 1 1.67E+09 1.67E+09 410.179 0.000Residual 50 2.03E+08 4.07E+06
Total 51 1.87E+09
![Page 31: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/31.jpg)
0
5
10
15
20
25
Residual Range
Histogram of Residuals
Residual
Theoretical
?),0( likelook residuals theDo 2N
![Page 32: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/32.jpg)
Line Fit P lot
-850
4150
9150
14150
19150
24150
29150
34150
39150
5000 15000 25000 35000 45000 55000 65000 75000
SquareF eet
Actual
P redicted
Upper 95%Lower 95%
Prediction Region
![Page 33: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/33.jpg)
Slide Typo Correction:Slide Typo Correction:2x2 Contingency Tables2x2 Contingency Tables
![Page 34: Last time: One-way Analysis of Variance. Example List of 50 spoken words 3 x 10 Subjects (split among I=3 groups) Group 1: (Fast sound) Person in movie.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649e4f5503460f94b4729d/html5/thumbnails/34.jpg)
Special Case: 2x2 Tables
1df with Square-Chi toCompare
:
2121
221122211
2
2
)2(1)1(10
CCRR
NNNNn
E
-ENΧ
ppH
i,j ij
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