# load diabetes.data

using CSV

Diabete_Data = CSV.read("diabetes.data"; datarow = 2, delim='\t',types=fill(Float64,11));

n,d = size(Diabete_Data);
d = d-1;

Diabete_Data

	AGE	SEX	BMI	BP	S1	S2	S3	S4	S5	S6	Y
1	59.0	2.0	32.1	101.0	157.0	93.2	38.0	4.0	4.8598	87.0	151.0
2	48.0	1.0	21.6	87.0	183.0	103.2	70.0	3.0	3.8918	69.0	75.0
3	72.0	2.0	30.5	93.0	156.0	93.6	41.0	4.0	4.6728	85.0	141.0
4	24.0	1.0	25.3	84.0	198.0	131.4	40.0	5.0	4.8903	89.0	206.0
5	50.0	1.0	23.0	101.0	192.0	125.4	52.0	4.0	4.2905	80.0	135.0
6	23.0	1.0	22.6	89.0	139.0	64.8	61.0	2.0	4.1897	68.0	97.0
7	36.0	2.0	22.0	90.0	160.0	99.6	50.0	3.0	3.9512	82.0	138.0
8	66.0	2.0	26.2	114.0	255.0	185.0	56.0	4.55	4.2485	92.0	63.0
9	60.0	2.0	32.1	83.0	179.0	119.4	42.0	4.0	4.4773	94.0	110.0
10	29.0	1.0	30.0	85.0	180.0	93.4	43.0	4.0	5.3845	88.0	310.0
11	22.0	1.0	18.6	97.0	114.0	57.6	46.0	2.0	3.9512	83.0	101.0
12	56.0	2.0	28.0	85.0	184.0	144.8	32.0	6.0	3.5835	77.0	69.0
13	53.0	1.0	23.7	92.0	186.0	109.2	62.0	3.0	4.3041	81.0	179.0
14	50.0	2.0	26.2	97.0	186.0	105.4	49.0	4.0	5.0626	88.0	185.0
15	61.0	1.0	24.0	91.0	202.0	115.4	72.0	3.0	4.2905	73.0	118.0
16	34.0	2.0	24.7	118.0	254.0	184.2	39.0	7.0	5.037	81.0	171.0
17	47.0	1.0	30.3	109.0	207.0	100.2	70.0	3.0	5.2149	98.0	166.0
18	68.0	2.0	27.5	111.0	214.0	147.0	39.0	5.0	4.9416	91.0	144.0
19	38.0	1.0	25.4	84.0	162.0	103.0	42.0	4.0	4.4427	87.0	97.0
20	41.0	1.0	24.7	83.0	187.0	108.2	60.0	3.0	4.5433	78.0	168.0
21	35.0	1.0	21.1	82.0	156.0	87.8	50.0	3.0	4.5109	95.0	68.0
22	25.0	2.0	24.3	95.0	162.0	98.6	54.0	3.0	3.8501	87.0	49.0
23	25.0	1.0	26.0	92.0	187.0	120.4	56.0	3.0	3.9703	88.0	68.0
24	61.0	2.0	32.0	103.67	210.0	85.2	35.0	6.0	6.107	124.0	245.0
25	31.0	1.0	29.7	88.0	167.0	103.4	48.0	4.0	4.3567	78.0	184.0
26	30.0	2.0	25.2	83.0	178.0	118.4	34.0	5.0	4.852	83.0	202.0
27	19.0	1.0	19.2	87.0	124.0	54.0	57.0	2.0	4.1744	90.0	137.0
28	42.0	1.0	31.9	83.0	158.0	87.6	53.0	3.0	4.4659	101.0	85.0
29	63.0	1.0	24.4	73.0	160.0	91.4	48.0	3.0	4.6347	78.0	131.0
30	67.0	2.0	25.8	113.0	158.0	54.2	64.0	2.0	5.2933	104.0	283.0
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

# compute the optimal theta

X = zeros(n,d);
y = zeros(n,1);

for i=1:d
    X[:,i] = Diabete_Data[:,i];
end
X = [ones(n,1) X];
y = Diabete_Data[:,end];

theta_opt = X\y

11-element Array{Float64,1}:
 -334.567    
   -0.0363612
  -22.8596   
    5.60296  
    1.11681  
   -1.09     
    0.74645  
    0.372005 
    6.53383  
   68.4831   
    0.280117 

# achieved loss

MSE = norm(X*theta_opt-y,2)^2/n

2859.6963475867506

# plot

using PyPlot;

figure();
plot(y,y,"k");
plot(y,X*theta_opt,"o",alpha=0.4);
xlabel("y");
ylabel("predicted y")
axis("square");
grid("on");

/usr/local/lib/python2.7/dist-packages/matplotlib/cbook/deprecation.py:107: MatplotlibDeprecationWarning: Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.
  warnings.warn(message, mplDeprecation, stacklevel=1)

# put JHK data into your predictor

#age
#sex
#bmi
#map	   mean arterial pressure				
#s1  tc :   total cholesterol
#s2  ldl    low density lipoprotein
#s3  hdl    high density lipoprotein
#s4  tch
#s5  ltg
#s6  glu
#        age  sex  bmi    map   tc     ldl    hdl     tch   ltg   glu
X_JHK = [41   1    18.3   90    171    80.0   74.9    2     4.75  90.0];
X_JHK = [1 X_JHK];

y_JHK = X_JHK*theta_opt

1-element Array{Float64,1}:
 108.892

# plot

using PyPlot;

figure();
plot(y,y,"k");
plot(y,X*theta_opt,"o",alpha=0.4);
plot(y_JHK,y_JHK,"ro",alpha=0.4)
xlabel("y");
ylabel("predicted y")
axis("square");
grid("on");