We know the values of x and y.  An equation has to be derived for the set of values.

We are all familiar with the equation y = m x + c

m is known as the slope and 
c as the intercept

We first find the average value of x and y.

For i in 1..n, we have 

AVG(x) = Σ xi/n  = (1+2+3+4+5)/5 = 15/5 = 3 
AVG(y) = Σ yi/n  = (13+5+6+6+4)/5 = 34/5 = 6.8

m = Σ (xi - AVG(x)) * (yi - AVG(y)) / Σ ((xi - AVG(x))2)

c = AVG(y) - m * AVG(x)

Start with the numerator (NR) of m: Σ(xi - AVG(x)) * (yi - AVG(y))

NR = (1-3)(13-6.8)+(2-3)(5-6.8)+(3-3)(6-6.8)+(4-3)(6-6.8)+(5-3)(4-6.8)
   = (-2)(6.2) + (-1)(-1.8) + (0)(-0.8) + (1)(-0.8) + (2)(-2.8)
   = (-12.4) + (1.8) + (0) + (-0.8) + (-5.6)
   = -17

The numerator also represents the Covariance(x,y)

Denominator (DR) of m: Σ (xi - AVG(x))2

DR = (1-3)2 + (2-3)2 + (3-3)2 + (4-3)2 + (5-3)2
  = 4 + 1 + 0 + 1 + 4
  = 10

 m = -17/10 = -1.7

 c = 6.8 - (-1.7)(3)
   = 11.9

 The equation y = m x + c becomes

 y = -1.7 x + 11.9
   = 11.9 - 1.7x

 RMSE = √ (ypi - y)2/n

 (ypi - y) = (13-10.2)2 + (8.5-5)2 + (6.8-6)2 + (5.1-6)2 + (3.4-4)2

           = (-2.8)2 + (3.5)2 + (0.8)2 + (-0.9)2 + (-0.6)2

           = 7.84 + 12.25 + 0.64 + 0.81 + 0.36 = 21.9

  RMSE = √ 21.9/5 = SQRT(21.9/5)

       = 2.0928449536