Problem Description:

This lab question is from optional textbook with minor modification.

The predictive task in this question is to predict the level of corruption in a country based on a range of macro-economic and social features. The table below lists some countries described by the following descriptive features:

• LIFE EXP., the mean life expectancy at birth
• TOP-10 INCOME, the percentage of the annual income of the country that goes to the top 10 percent of earners
• INFANT MORT., the number of infant deaths per 1,000 births
• MIL. SPEND, the percentage of GDP spent on the military
• SCHOOL YEARS, the mean number years spent in school by adult females

The target feature is the Corruption Perception Index (CPI). The CPI measures the perceived levels of corruption in the public sector of countries and ranges from 0 (highly corrupt) to 10 (very clean).

The data listed in this table is real and is form 2010/11 (or the most recent year prior to 2010/11 when the data was available).

The data for the descriptive features in this table was amalgamated from a number of surveys retrieved from Gapminder (www.gapminder.org). The Corruption Perception Index is generated annually by Transparency International (www.transparency.org).)

COUNTRY	LIFE EXP.	TOP-10 INCOME	INFANT MORT.	MIL. SPEND	SCHOOL YEARS	CPI
Afghanistan	59.61	23.21	74.30	4.44	0.40	1.5171
Haiti	45.00	47.67	73.10	0.90	3.40	1.7999
Nigeria	51.30	38.23	82.60	1.97	4.10	2.4493
Egypt	70.48	26.58	19.60	1.86	5.30	2.8622
Argentina	75.77	32.30	13.30	0.76	10.10	2.9961
China	74.87	29.98	13.70	1.95	6.40	3.6356
Brazil	73.12	42.93	14.50	1.43	7.20	3.7741
Israel	81.30	28.80	3.60	6.77	12.50	5.8069
U.S.A.	78.51	29.85	6.30	4.72	13.70	7.1357
Ireland	80.15	27.23	3.50	0.60	11.50	7.5360
U.K.	80.09	28.49	4.40	2.59	13.00	7.7751
Germany	80.24	22.07	3.50	1.31	12.00	8.0461
Canada	80.99	24.79	4.90	1.42	14.20	8.6725
Australia	82.09	25.40	4.20	1.86	11.50	8.8442
Sweden	81.43	22.18	2.40	1.27	12.80	9.2985
New Zealand	80.67	27.81	4.90	1.13	12.30	9.4627

We will use Russia as our query country for this question. The table below lists the descriptive features for Russia.

COUNTRY	LIFE EXP.	TOP-10 INCOME	INFANT MORT.	MIL. SPEND	SCHOOL YEARS	CPI
Russia	67.62	31.68	10.00	3.87	12.90	?

Your tasks:

1. Calculate the distance between Russia and each of the countries listed in the first table using Euclidean distance.
2. What value would a 3-nearest neighbor prediction model using Euclidean distance return for the CPI of Russia?
3. What value would a weighted k-NN prediction model return for the CPI of Russia? Use k = 3 and k = 16 (i.e., the full dataset) respectively and a weighting scheme of the reciprocal of the squared Euclidean distance between the neighbor and the query.
4. The descriptive features in this dataset are of different types. For example, some are percentages, others are measured in years, and others are measured in counts per 1,000. We should always consider normalizing our data, but it is particularly important to do this when the descriptive features are measured in different units. Generate a new table of data for the countries (including Russia), where each descriptive attribute is normalized using range normalization.
5. What value would a 3-nearest neighbor predicion model using Euclidean distance return for the CPI of Russia when the descriptive features have been normalized using range normalization?
6. What value would a weighted k-NN prediction model return for the CPI of Russia when it is applied to the range-normalized data? Use k = 3 and k = 16 (i.e., the full dataset) respectively and a weighting scheme of the reciprocal of the squared Euclidean distance between the neighbor and the query.
7. The actual 2011 CPI for Russia was 2.4488. Which of the predictions made was the most accurate? Why do you think this was?