MATH235 MATH235 Week 6 - Assessed problems (coursework) MATH235 Week 7 - Workshop problems

MATH235 Week 6 - Moodle Quiz-assessed problems

Data on fertility rates in different countries are contained in the UN2 dataset. We will fit two regression models to these data, and compare the fit of the models to see whether the (log) per person gross domestic product (logPPgdp) (only) or both the (log) per person gross domestic product (logPPgdp) and the percentage of the population that lives in an urban area (Purban) can be used to explain variability in the log fertility of the set of countries (logFertility). In what follows, let $Y_{i}$ denote the log fertility rate, $x_{i,1}$ denote log per person GDP and $x_{i,2}$ denote the percentage in urban areas:

	$\displaystyle\mathbb{E}[Y_{i}]$	$\displaystyle=$	$\displaystyle\beta_{1}+\beta_{2}x_{i,1}$		(0.7)
	$\displaystyle\mathbb{E}[Y_{i}]$	$\displaystyle=$	$\displaystyle\beta_{1}+\beta_{2}x_{i,1}+\beta_{3}x_{i,2}$		(0.8)

Use the $F$ -test to compare Models 0.7 and 0.8.

Q6.1

Least squares estimates
The least squares coefficients for the logPPgdp covariate are

(a)

-0.523 for Model 0.7 and -0.234 for Model 0.8.
(b)

-0.234 for Model 0.7 and -0.523 for Model 0.8.
(c)

-0.234 for Model 0.7 and -0.221 for Model 0.8.
(d)

-0.221 for Model 0.7 and -0.181 for Model 0.8.
(e)

-0.181 for Model 0.7 and -0.221 for Model 0.8.

[marks: 2]

Q6.2

Sums of squares
The sums of squares for the two models are

(a)

56.24 and 53.91
(b)

62.43 and 56.16
(c)

62.40 and 61.27
(d)

65.72 and 63.63
(e)

72.25 and 68.55

[marks: 2]

Q6.3

Test statistic
What is the value of the test statistic to test the suitability of Model 0.7 against Model 0.8?

(a)

2.459
(b)

2.676
(c)

2.874
(d)

3.091
(e)

3.494

[marks: 2]

Q6.4

Critical value
Assuming a 5% significance level, what is the critical value for this test?

(a)

2.65
(b)

3.04
(c)

3.89
(d)

5.10
(e)

5.32

[marks: 2]

Q6.5

p value
What is the $p$ -value for your test?

(a)

0.063
(b)

0.036
(c)

0.079
(d)

0.097
(e)

0.044

[marks: 2]