You should define x as a vector recording the data for the GDP and y as a vector recording the life satisfaction index. You can save your data into a ‘mat’ file by the MATLAB function save(’data.mat’,’x’,’y’). Next time when you retrieve the data, use the MATLAB function load(’data.mat’). Perform the following tasks

San Diego State University – Department of Electrical and Computer Engineering

EE300 – Computational and Statistical Methods of Electrical Engineers

Fall 2018 – MATLAB Project

The following dataset was obtained from the Organization for Economic Cooperation and Development (OECD) website on the Gross Domestic Product (GDP) per capita and the Life Satisfaction Index (LSI) of the following countries:

Index	Country	GDP in	Life Satisfac-
		$1000 USD	tion Index (LSI)
1.	Australia	33.4	7.3
2.	Austria	32.5	7
3.	Belgium	30.0	6.9
4.	Canada	29.9	7.3
5.	Chile	16.6	6.7
6.	Czech Republic	21.1	6.6
7.	Denmark	29.0	7.5
8.	Estonia	18.7	5.6
9.	Finland	29.5	7.5
10.	France	31.1	6.4
11.	Germany	33.7	7
12.	Greece	17.0	5.2
13.	Hungary	16.8	5.3
14.	Iceland	30.5	7.5
15.	Ireland	25.4	7
16.	Israel	24.0	7.2
17.	Italy	26.1	5.9
18.	Japan	28.6	5.9
19.	Korea	21.7	5.9
20.	Latvia	15.3	5.9
21.	Luxembourg	41.3	6.9
22.	Mexico	13.9	6.6
23.	Netherlands	28.8	7.4
24.	New Zealand	24.4	7.3
25.	Norway	35.7	7.5
26.	Poland	18.9	6
27.	Portugal	20.5	5.2
28.	Slovak Republic	20.2	6.1
29.	Slovenia	20.5	5.8
30.	Spain	23.1	6.4
31.	Sweden	30.6	7.3
32.	Switzerland	36.4	7.5
33.	Turkey	17.1	5.5
34.	United Kingdom	28.4	6.7
35.	United States	44.0	6.9
36.	Brazil	12.2	6.6
37.	Russia	16.7	6
38.	South Africa	10.9	4.8

You should define x as a vector recording the data for the GDP and y as a vector recording the life satisfaction index. You can save your data into a ‘mat’ file by the MATLAB function save(’data.mat’,’x’,’y’).

Next time when you retrieve the data, use the MATLAB function load(’data.mat’). Perform the following tasks:

Find the (sample) means of the GDP and the LSI and store them as m_Xand m_Y.

Suggestion: You may wish to try the MATLAB functions mean(x) and mean(y).

Find the (sample) standard deviation of the GDP and the LSI and store them as std_Xand std_Y.

Suggestion: You may wish to try the MATLAB functions std(x) and std(y).

Find the range (i.e., the maximum and the minimum values) of the GDP.

Suggestion: You may wish to try the MATLAB functions max(x), min(x) and range(x).

Divide the range into N = 8 equal-length segments (hereafter called “bins”) and for each bin, find its bound (a_j,b_j) as well as its center c_jfor j = 1,2,…,

Suggestion: It might be convenient to store a_j’s in a vector a, b_j’s in a vector b and c_j’s in a vector c with an appropriate length.

Sort the data and place each GDP value x_iinto that bin whose lower bound is less than or equal to x_iand whose upper bound is greater than x_i; thereafter, for each bin count the number of x_iassigned to it (= n_j).
(2pt) Plot a histogram of the measured GDP using N = 8 bars.

Suggestion: You may wish to try the MATLAB functions hist(x,N) and bar(c,n).

Produce a vector x_aof the recorded GDP in which the numbers are arranged in ascending order.
(2pt) Determine the median of the GDPs by writing a script that is usable for both odd and even number of samples. Print your result and compare it with the result obtained from the MATLAB function median(x).
Define a random variable W as the GDP of a randomly selected country, and estimate (i.e., determine approximately) the probability mass function of this random variable, evaluated at the each of the bin centers c_j.
Estimate the (cumulative) probability distribution function of the same random variable W, evaluated at the same points (i.e., argument values) c_j.

Suggestion: You may wish to try the MATLAB function cumsum(n)/sum(n).

(2pt) Produce a plot of the cumulative probability distribution function (found above) as a function of its argument, in which the plot has a title, axes have a scale and a label, and the graph is piece-wise linear plot between points at the bin centers.
(2pt) Illustrate the data in the table using a scatter plot with the horizontal axis representing the GDP and the vertical axis representing the LSI. From the plot, determine whether the GDP and the LSI have positive correlation, negative correlation or no correlation.

Suggestion: You may wish to try the MATLAB function scatter(x,y).

Find the sample covariance of the GDP and the LSI and store it as cov_XY.

Suggestion: You may wish to try the MATLAB command n/(n − 1) ∗ mean((x − mx). ∗ (y − my)).

(2pt) Find the correlation coefficient from the sample covariance and the standard deviations of the GDP and the LSI. Print the obtained correlation coefficient, and determine if the calculation confirms with your observation from the scatter plot.

Please turn in your MATLAB script in one section and the results/plots in another section. Deadline: Dec 17, 2018. Please place the hard copy under the door of E-408 office.

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