column1 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column2 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column3 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column4 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column5 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column6 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0
column7 = array (0, dim=c(1))
for (i in 1:k) column1[i]=0

df6 = data.frame (one=column1, two=column2, three=column3, four=column4, five=column5, six=column6, seven=column7) # для частот

xx=a$Writing.Mean # начальные x
yy=a$Mathematics.Mean # начальные y

df
NN = 0 # для проверки
kk = k-1
#заполняем таблицу частот
for (i in 1:N) {
    for (j in 1:kk) {
        if ((xx[i]>=df$From[j])&&(xx[i]<df$To[j])) {
            for (p in 1:kk) {
                if ((yy[i]>=df5$From[p])&&(yy[i]<df5$To[p])) {
                    df6[p,j]=df6[p,j]+1
                    NN = NN +1
                    }
            }
            if ((yy[i]>=df5$From[k])&&(yy[i]<=df5$To[k])) {
                    df6[k,j]=df6[k,j]+1
                    NN = NN +1
                    }
        }

    }
    if ((xx[i]>=df$From[k])&&(xx[i]<=df$To[k])) {
            for (p in 1:kk) {
                if ((yy[i]>=df5$From[p])&&(yy[i]<df5$To[p])) {
                    df6[p,k]=df6[p,k]+1
                    NN = NN +1
                    }
            }
            if ((yy[i]>=df5$From[k])&&(yy[i]<=df5$To[k])) {
                    df6[k,k]=df6[k,k]+1
                    NN = NN +1
                    }
        }
}

df6 #таблица частот

############
x_kryshka = array(0, dim=c(1))
x_kryshka[1] = 0
x_kryshka[2] = 0
x_kryshka[3] = 0
x_kryshka[4] = 0
x_kryshka[5] = 0
x_kryshka[6] = 0
x_kryshka[7] = 0
for (i in 1:k)
    for (j in 1:k) {
        x_kryshka[i] = x_kryshka[i] +x[j]*df6[i,j]
    }
x_kryshka

wxy = 0
for (i in 1:k)
    wxy = wxy + y[i]*x_kryshka[i]

wxy
##########
y_kryshka = array(0, dim=c(1))
y_kryshka[1] = 0
y_kryshka[2] = 0
y_kryshka[3] = 0
y_kryshka[4] = 0
y_kryshka[5] = 0
y_kryshka[6] = 0
y_kryshka[7] = 0
y_kryshka
for (j in 1:k)
    for (i in 1:k) {
        y_kryshka[j] = y_kryshka[j] +(y[i]*df6[i,j])
    }
y_kryshka

wxy2 = 0
for (i in 1:k)
    wxy2 = wxy2 + x[i]*y_kryshka[i]

wxy2
##########
wxy3 = 0
for (i in 1:k)
    for (j in 1:k)
        wxy3=wxy3+df6[i,j]*x[j]*y[i]
wxy3
##########

mxy = wxy/N - xsr*ysr
mxy


rxy = mxy/(S*S2)
rxy

# доверительный интервал для коэффициента корреляции

z = 0.5 * log (((1+rxy)/(1-rxy)), base = exp(1))
SE = (k-3)^(-1/2)
SE
T_krit = 2.57
z1 =  z - T_krit*SE
z2 =  z = T_krit*SE
tanh(z1) #интервал от этого числа
tanh(z2) #и до этого

# проверка статистической гипотезы о равенстве коэффициента корреляции нулю

T_nabl = rxy * (sqrt(k-2)/sqrt(1-rxy^2))
T_nabl

T_krit = 2.57