Class Notes
(808,754)

Canada
(493,378)

University of Ottawa
(32,193)

Administration
(2,631)

ADM2304
(69)

Tony Quon
(67)

Lecture 20

#
ADM2304 Lecture 20: 20
Premium

Unlock Document

University of Ottawa

Administration

ADM2304

Tony Quon

Fall

Description

Two Key Intervals
1.C.I. for the mean of Y at a given value of X
2. Prediction interval (P.I.) for a future observation of Y at a given value of X
For a given x*, which interval will be bigger?
P.I. since the mean varies less than a given observation
Same point estimate for both! *
y =b +b x
x* 0 1
Two Key Intervals
If the extrapolation penalty is small and n is reasonably large, then an approximate 95%
P.I. is:
y *2s
x
Why do both the C.I. and the P.I. increase in size as you move away from the mean of
X? Summary
Model of population: y = β +β x +ε
i 0 1 i i
4 Assumptions:
Linearity, constant variance, normality and independence
Unfortunately, we don’t know 0, 1 or 2 so we take a sample (x1,y1),…,(xn,yn)
and get sample estimates b0, b1 and s2 from which we can get C.I. and perform
hypothesis tests to determine if there is a linear relationship
What we are really interested in is estimating Y so we look at:
1. C.I. for the mean of Y for a given x*
2. P.I. for a future observed Y at a given x*
Inference for Simple Linear Regression (Cont’d)
Two Key Intervals:
1. C.I. for the mean of Y at a given value of X
2. Prediction interval (P.I.) for a future observation of Y at a given value of X
For a given x*, which interval will be bigger?
P.I. since the mean varies less than a given observation
Same point estimate for both: ! *
y =* +b x
x 0 1
C.I.for µ Y | x
2
* 1 (x − x)
b0+b 1 ±t α /2,n−2 n+ 2
∑ (xi− x)
P.I.forY | x
* 1 x − x)2
b0+b 1 ±t α /2,n−21+ + 2
n ∑ (xi− x)
Two Key Intervals:
If the extrapolation penalty is small and n is reasonably large, then an approximate 95%
P.I. is:
⌢
y *2s
x
Why do both the C.I. and the P.I. increase in size as you move away from the mean of
X? Example: Resurfacing Contract
The director of a highway department wants to predict the cost of a resurfacing contract
that is up for bids (6-km road)
The cost could be predicted as a function of the kilometers of road to be resurfaced
Past contracts from various bidders gives the following data:
Cost (Y) in $10,000 6 14 10 14 26
Distance (X) in km. 1 3 4 5 7
∑ x = 20 ∑ y = 70 ∑ xy =340 x = 4 C.I. for the average cost of a

More
Less
Related notes for ADM2304