# part 1

mydata = read.csv("lqmt_6month.csv");

names(mydata)

n = length(mydata$Date);
myday = c(1:n)

x = myday;
y = rev(mydata$High);

sx = sd(x);
sy = sd(y);

plot(myday, rev(mydata$High),pch=20,xlab="day number",ylab="high stock price")
title(main="Daily High Price of LQMT stock", col.main="red", font.main=4)



xbar = mean(x);
ybar = mean(y);

z = ((x - xbar)/sx)*((y - ybar)/sy)

print("correlation coefficient is:")
corval = sum(z)/(length(x) - 1);
print(corval)

print("calculating least squares fit:")
n = length(x);
x2 = x^2;
xy = x*y;
nxy = n*xy;

sumx = sum(x); 
sumy = sum(y);
sumxy = sum(xy);
sumx2 = sum(x2);

m = (n*sumxy - sumx*sumy)/(n*sumx2 - sumx^2);

b = (sumx2*sumy - sumxy*sumx)/(n*sumx2 - sumx^2)

print("plotting line:")
abline(a=b,b=m,col="blue",lwd=3)

print("check against R result:");
fit <- lm(y ~ x)


# part 2


x=c(1,5,0.5,0.8,6,20,42,0.001,4,0.6,31,12,3,0.5,10,12,9,8,15,1)
xbar = mean(x)
# 9.07005
n = length(x)
#[1] 20
s=sd(x)
#[1] 11.06722
var(x)
#122.4834
sd(x)^2
#122.4834

xs = sort(x)

L25 = (25/100)*n;
# 5 -> whole number
Q1 = (xs[L25] + xs[L25+1])/2

L50 = (50/100)*n;
# 10 -> whole number
Q2 = (xs[L50] + xs[L50+1])/2

L75 = (75/100)*n;
# 15 -> whole number
Q3 = (xs[L75] + xs[L75+1])/2

minval = min(x);

maxval = max(x);

print("five number summary: min, Q1, Q2, Q3, max");
print(minval);
print(Q1);
print(Q2);
print(Q3);
print(maxval);

iqr = Q3- Q1;
lbnd = Q1 - 1.5*iqr
rbnd = Q3 + 1.5*iqr

print("xbar +- 2*s = ");
print(c(xbar - 2*s, xbar + 2*s));
bnd1 = xbar - 2*s; 
bnd2 = xbar + 2*s;
sum(x>=bnd1 & x<=bnd2)
# 19 of 20
pt = sum(x>=bnd1 & x<=bnd2)/n * 100
# 95 %