Question 1 :

The percentage of youth not in employment, education or training (NEET) is of greater policy significance than simply looking at unemployment rates. We hypothesise that NEET is influenced by the average age at which females are having their first child and their school life expectancy. Data is collected for 30 countries in NEET.

Country	NEET	Mean Birth age	School life expectancy
Netherlands	4.4	28.9	15.9
Denmark	5.6	29.1	15.6
Iceland	5.9	27	15.8
Switzerland	6.8	30.2	15
Sweden	6.8	28.6	16
Austria	6.8	28.5	14.7
Slovenia	7.4	28.7	14.1
Luxembourg	7.9	29.3	13.1
Finland	8.6	27.9	16.7
Canada	8.8	27.6	14.8
Norway	9.2	28.4	16.9
Germany	9.5	28.9	15.3
Japan	10.1	29.4	14.3
Czech Republic	11.0	27.6	13.5
Estonia	11.0	26.3	14.1
Poland	11.1	26.6	14.4
Australia	11.4	30.5	16.6
France	12.0	28.6	15.4
New Zealand	12.5	27.7	16.2
Portugal	12.8	27.4	15.2
United Kingdom	13.4	30	16.4
Hungary	13.8	28.2	13.6
United States	14.8	25	15.2
Belgium	16.0	28	15.8
Ireland	17.6	29.8	14.9
Spain	17.6	29.3	15.3
Greece	18.2	29.2	14.3
Italy	19.5	27.7	14.7
Mexico	22.0	21.3	11.5
Turkey	30.2	22.9	9.5

a State the multiple regression equation. b. Interpret the meaning of the slopes in this equation. c. Predict the percentage of youth not in employment, education or training (NEET) for a country where the mother's average age at first birth is 25 and school life expectancy is 15 years. d. Is there a significant relationship between NEET and the two independent variables at the 0.05 level of significance? e. Interpret the meaning of the coefficient of multiple determination. f. Determine the adjusted R 2. g. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model.

Question 2

An experiment was conducted to study the extrusion process of biodegradable packaging foam (data extracted from W. Y. Koh, K. M. Eskridge and M. A. Hanna, 'Supersaturated split-plot designs', Journal of Quality Technology, 45, January 2013, 61-72). Among the factors considered for their effect on the unit density (mg/mL) were the die temperature (145 C versus 155 C) and the die diameter (3 mm versus 4 mm). The results were stored in . Develop a multiple regression model that uses die temperature and die diameter to predict the unit density (mg/mL). Do you think that you need to use both independent variables in the model? Explain.

Packaging foam3 figure :

Die Diameter Foam Density 72.54 (a) 1 = 2917.00 53.60 48.13 2 = 3801 69.89 3 = 4384.5 3 62.78 55.18 4 = 8745 57.22 5 = 10064 66.70 49.28 The better choice would be 5. 44.14 58.37 53.98 57.50 3 54.17 (b) The problem in (a) is that the regression 73.86 model is a constant linear growth trend and 90.28 88.19 even if the values in (a) are within the range 82.61 of the data, it would follow that sales would 63.03 4 46.73 increase as both salary and commission 60.17 increase. However, this may not be realistic 46.78 4 43.27 in a real-world setting. 56.93