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.