Statistics: Linear Regression, ANOVA, Hypothesis Testing

Running Head: STATISTICS
Statistics
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1STATISTICS
Table of Contents
Answer 1..........................................................................................................................................3
1.a)................................................................................................................................................3
1.a.i)..........................................................................................................................................3
1. a.ii)........................................................................................................................................3
1.a.iii)........................................................................................................................................3
1. b)..............................................................................................................................................4
1.b.i)..........................................................................................................................................4
1.b.ii)........................................................................................................................................4
1.b.iii).......................................................................................................................................5
1.c)................................................................................................................................................6
1.c.i)..........................................................................................................................................7
1.c.ii).........................................................................................................................................7
1.c.iii)........................................................................................................................................7
1.d.................................................................................................................................................7
1.d.i)..........................................................................................................................................7
1.d.ii)........................................................................................................................................7
1.e)................................................................................................................................................8
1. f)...............................................................................................................................................9
1. f. i)........................................................................................................................................9
1. f. ii).....................................................................................................................................11
Answer 2........................................................................................................................................12
2.a)..............................................................................................................................................12
2.b).............................................................................................................................................13
2.b.i)........................................................................................................................................13
2.b.ii)......................................................................................................................................13
Answer 3........................................................................................................................................13
3.a)..............................................................................................................................................13
3.b).............................................................................................................................................13

2STATISTICS
3.b.i)........................................................................................................................................14
3.b.ii)......................................................................................................................................14
Answer 4........................................................................................................................................14
Answer 5........................................................................................................................................14
5.a)..............................................................................................................................................14
5. b)............................................................................................................................................14
5.b.i)........................................................................................................................................15
5.b.ii)......................................................................................................................................15
5.b.iii).....................................................................................................................................15
5.b.iv)......................................................................................................................................15
5.c)..............................................................................................................................................15
5.d).............................................................................................................................................16
5.d.i)........................................................................................................................................17
5.d.ii)......................................................................................................................................17
5.d.iii).....................................................................................................................................17
5.d.iv)......................................................................................................................................17
5.e)..............................................................................................................................................17
References:....................................................................................................................................19

3STATISTICS
Answer 1.
1.a)
1.a.i)
M0: yij = α + Ԑij.
For model M0, the design matrix X and vector parameter β in the matrix are-
Race (i) and β = 1.5319.
1. a.ii)
M1: yij =a +β1xij +β2wij +eij
For model M1, the design matrix X are-
Smoke (xij) and Lwtkg (wij)
The vector parameters (β) in the matrix are respectively-
β1 = -0.44314 and β2 = 0.00556.
1.a.iii)
M2: yij =a + β1xij + β2wij + τi + eij