Stat 141 R1 - Lecture #35
Announcements:
1) Assignment #11 Question 5:
The answer is wrong … should be “fail to reject” but MyStatLab wants “reject”... so give the wrong answer for full marks in this question
2) Exam:
STAT 141 R1 3 hrs 1400 Wed Apr 17 MAIN GYM,
~45 Multiple Choice Questions
Chapters 7, 8, 18-28 …. some pre MT skills will be required.
Simple Linear Regression …. continued

Last time:

Ex) Predicting final exam marks (%) from midterm exam marks (%) in a class of 88 students:

Student | #1 | #2 | … | #88 | Midterm mark | 67% | 72% | … | 88% | Final mark | 62% | 50% | … | 91% |

Stat 141 R1 - Lecture #35 page 2

Given x = midterm percentage, y = final percentage,

n=88, x = 67.812, y = 52.643, sx = 17.922, sy = 25.430, r = 0.718
∑(yi–ŷi)2 = 27278.82

We had calculated:

The slope and intercept of the sample line of best fit:

* sample line of best fit: y= -16.443 + 1.019 x

An estimate for σ (standard deviation about the population line): se

Given SSE = ∑(yi–ŷi)2 = 27278.82 :

se2=SSEn-2=27278.8288-2=317.196
→σ≈se=317.196=17.810
Stat 141 R1 - Lecture #35 page 3

Inference for the population slope β1

When the 4 basic assumptions of the SLR model are satisfied:

o The relationship between x and y is sufficiently linear. Presuming linearity, this means, at any x, με = 0. o The std. dev. of ε is the same for any particular x (constant). o The distribution of ε at any particular x is normal. o The random deviations ε1, ε2, ..., εn associated with different observations are independent of one another.

then: i) b1 is normally distributed

ii) The mean of b1 is μb1 = β1

iii) The standard deviation of b1 is σb1=σ(xi-x)2

The standard error of b1 is SEb1=se(xi-x)2=sesxn-1

* CI for β1: b1± tα/2× SE(b1)