MATH235 MATH235 Week 6 - Workshop problems MATH235 Week 6 - Moodle Quiz-assessed problems

MATH235 Week 6 - Assessed problems (coursework)

Submission is due on Tuesday in Week 7.

We have looked several times at the Olympic data, first introduced in Question Sheet 3. This data set contains winning high jump heights, long jump distances and discus throws at a sample of ten Olympics. The aim was to see which of long jump ( $x_{i,1}$ ) and discus throw ( $x_{i,2}$ ) could be used to predict high jump heights ( $Y_{i}$ ).

Consider the three possible models

$\displaystyle\mathbb{E}[Y_{i}]$	$\displaystyle=$	$\displaystyle\beta_{1}+\beta_{2}x_{i,1},$	(0.4)
$\displaystyle\mathbb{E}[Y_{i}]$	$\displaystyle=$	$\displaystyle\beta_{1}+\beta_{2}x_{i,2},$	(0.5)
$\displaystyle\mathbb{E}[Y_{i}]$	$\displaystyle=$	$\displaystyle\beta_{1}+\beta_{2}x_{i,1}+\beta_{3}x_{i,2}.$	(0.6)

CW6.1

(a)

Define what is meant by the ‘sum of squares’ of a fitted model.

[marks: 1]

The sums of squares for these models are 74.18, 52.36 and 50.10 respectively.
(b)
Use the $F$ -test to compare
- (i)
  
  Models 0.4 and 0.6,
  
  [marks: 4]
- (ii)
  
  Models 0.5 and 0.6.
  
  [marks: 4]
Which is your preferred model in each case?
(c)

Why is this test not appropriate for a comparison of models 0.4 and 0.5?

[marks: 1]