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ch04.jl
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# Bogumił Kamiński, 2021
# Codes for chapter 4
# Code for listing 4.1
aq = [10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
14.0 9.96 14.0 8.1 14.0 8.84 8.0 7.04
6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
4.0 4.26 4.0 3.1 4.0 5.39 19.0 12.50
12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89]
# Code for checking size of a matrix
size(aq)
size(aq, 1)
size(aq, 2)
# Code comparing tuple to a vector
v = [1, 2, 3]
t = (1, 2, 3)
v[1]
t[1]
v[1] = 10
v
t[1] = 10
# Code for figure 4.2
using BenchmarkTools
@benchmark (1, 2, 3)
@benchmark [1, 2, 3]
# Code for section 4.1.2
using Statistics
mean(aq; dims=1)
std(aq; dims=1)
map(mean, eachcol(aq))
map(std, eachcol(aq))
map(eachcol(aq)) do col
mean(col)
end
[mean(col) for col in eachcol(aq)]
[std(col) for col in eachcol(aq)]
# Code for section 4.1.3
[mean(aq[:, j]) for j in axes(aq, 2)]
[std(aq[:, j]) for j in axes(aq, 2)]
axes(aq, 2)
?Base.OneTo
[mean(view(aq, :, j)) for j in axes(aq, 2)]
[std(@view aq[:, j]) for j in axes(aq, 2)]
# Code for section 4.1.4
using BenchmarkTools
x = ones(10^7, 10)
@btime [mean(@view $x[:, j]) for j in axes($x, 2)];
@btime [mean($x[:, j]) for j in axes($x, 2)];
@btime mean($x, dims=1);
# Code for section 4.1.5
[cor(aq[:, i], aq[:, i+1]) for i in 1:2:7]
collect(1:2:7)
# Code for section 4.1.6
y = aq[:, 2]
X = [ones(11) aq[:, 1]]
X \ y
[[ones(11) aq[:, i]] \ aq[:, i+1] for i in 1:2:7]
function R²(x, y)
X = [ones(11) x]
model = X \ y
prediction = X * model
error = y - prediction
SS_res = sum(v -> v ^ 2, error)
mean_y = mean(y)
SS_tot = sum(v -> (v - mean_y) ^ 2, y)
return 1 - SS_res / SS_tot
end
[R²(aq[:, i], aq[:, i+1]) for i in 1:2:7]
?²
# Code for section 4.1.7
using Plots
scatter(aq[:, 1], aq[:, 2]; legend=false)
plot(scatter(aq[:, 1], aq[:, 2]; legend=false),
scatter(aq[:, 3], aq[:, 4]; legend=false),
scatter(aq[:, 5], aq[:, 6]; legend=false),
scatter(aq[:, 7], aq[:, 8]; legend=false))
plot([scatter(aq[:, i], aq[:, i+1]; legend=false)
for i in 1:2:7]...)
# Code for section 4.2
two_standard = Dict{Int, Int}()
for i in [1, 2, 3, 4, 5, 6]
for j in [1, 2, 3, 4, 5, 6]
s = i + j
if haskey(two_standard, s)
two_standard[s] += 1
else
two_standard[s] = 1
end
end
end
two_standard
keys(two_standard)
values(two_standard)
using Plots
scatter(collect(keys(two_standard)), collect(values(two_standard));
legend=false, xaxis=2:12)
all_dice = [[1, x2, x3, x4, x5, x6]
for x2 in 2:11
for x3 in x2:11
for x4 in x3:11
for x5 in x4:11
for x6 in x5:11]
for d1 in all_dice, d2 in all_dice
test = Dict{Int, Int}()
for i in d1, j in d2
s = i + j
if haskey(test, s)
test[s] += 1
else
test[s] = 1
end
end
if test == two_standard
println(d1, " ", d2)
end
end
# Code for section 4.3
aq = [10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
14.0 9.96 14.0 8.1 14.0 8.84 8.0 7.04
6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
4.0 4.26 4.0 3.1 4.0 5.39 19.0 12.50
12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89]
dataset1 = (x=aq[:, 1], y=aq[:, 2])
dataset1[1]
dataset1.x
# Code for listing 4.2
data = (set1=(x=aq[:, 1], y=aq[:, 2]),
set2=(x=aq[:, 3], y=aq[:, 4]),
set3=(x=aq[:, 5], y=aq[:, 6]),
set4=(x=aq[:, 7], y=aq[:, 8]))
# Code for section 4.3.2
using Statistics
map(s -> mean(s.x), data)
map(s -> cor(s.x, s.y), data)
using GLM
model = lm(@formula(y ~ x), data.set1)
r2(model)
# Code for section 4.3.3
model.mm
x = [3, 1, 3, 2]
unique(x)
x
unique!(x)
x
empty_field!(nt, i) = empty!(nt[i])
nt = (dict = Dict("a" => 1, "b" => 2), int=10)
empty_field!(nt, 1)
nt