Stat 88 Lec 40
today Review chap 12 simple and multiple regressionOverview of classmethod of indicators
ex
regressline
f Eri4BotBXTycheline
n 2327
To test the hypothesisHo B 0
HA BT B where fifty
use Tvs
Assuming the nonSE B
P ual PCIT1t
in standard units
r2p Val qzfo CI
SE T
Bo Bo
B IB
what can go conclude from this tableabout Bo B we accept null that Bo
and reject all that 4 0
If I dont give you E in this table can youfigure it out from the rest of the table
yes assuming the hull
t B 11.499114290.099
If I dont give you P let in this table can you
figure it out from the rest of the tablefor n large
we know t
P ual P It I 2 I OICH since a 232is large
and T m NcesEr 2ft stats t Cdf ft Ifs n 2
tsang
Can you find the 9540 CI for B fromthe table above
yes BT I 2 SE BT 13.18 I 2 6.864
Tor use stats t ppf f 975 If n 2
if n s30
My 91.295 18.78y
If I give you the info above can you findMy ad F
I rr E If9 9.920
Bo my Bmx my MIRO 94,3913.12 68.520
EI Surpose you have a scatter diagramgiven below should you make a linear regressionmodel Explain
A No our linear model
is y Bot B X t Ee
not having a constantvariance i.e variancebigger for bigger X
orI
see 12.3 Multiple regression
multiple regression generalizes simple linear regression0 more than one predictoret
Rest and Wgt will be predictorsNow
They should not be correlated r 18ok
I
Bo
B
Bz
what can you conclude from this tableaccent null for Bo Bz and reject for BRZ goes up just a little so ugt isnt contributing
to a better fit We should remove wgt from themodel since Be D
what Active pulse would you expect if you have
it Rest 50 and Wgt 150
Do t BT rest BengtGAY t 1.16150 t i03 150 6
overview of class inverse probone first day of classstatsI asked you which isProbability and whichis statistics
Prob
ProbabilityYou have learned both discrete and continuous
Probability distributiondiscrete continuous
analogous to Uniton 1 through N
analogous to Gears P
analogous toBinomial n P
You have learned how to calculate the expectationof quite complicated probability distributions using themethod of indicators Expectation is the center or
average of your data's histogram
You learned how that SD is the average spread of
your data from the mean
If we dont assume anything about the
Population distribution except the mean and SD
you can use Chebyshev inequality to get an
upperbound on the tail probabilityLarge sample approximations such as the
law of averages which says I Mx and
the CLT which says In NCMx is
very usefulInference Statistics
Given a sample from a population with one of
the above distributions you learned how to
estimate the parameter population
In the case of regression you learned how to
use the regression line to estimate the Tyche lobe
From our sample we can make hypotheses about
the value of the parameter of the population distributionAssuming the hull is true we compute a test
statistic and compute the p value If the
p value is less that a 05 for a n 05 level test
we reject the hull
A 9590 CI for an unknown Parameter
tells you whether you should reject the null
for the alternative
methodotindicatouthout
since the population size N isnt givenyou can assume it is infinite so drainingwith and uilthat replacement are quivalent
The solution then is ECHf.yjdtegjdt.se 49539 If 4see midterm review for detailsIf the problem tells you N 100then the answer is
X the of colors foot of 4 that do not appear
If 7 it green doesnt appear in d drainsq 0 else Lpgreen 6
similarly for other colors pg
i iY i iT S T 9
Blue Green yellow purple
In a box of tickets, 60% of the ticketsare blue, 20% green, 15% yellow, and 5%purple. Find the expected number of colorsthat do not appear among d draws made atrandom with replacement from the box.