Question

find the normal equation of regression for y=a+bx+cx2+dx3

Answer 1

hey user !!

Step-by-step explanation:

The formula for Regression Analysis –

Y = a + bX + ∈

Y = Stands for the dependent variable

X = Stands for an independent variable

a = Stands for the intercept

b = Stands for the slope

∈ = Stands for the error term

The formula for intercept “a” and the slope “b” can be calculated as per below.

a = (Σy)(Σx2) – (Σx)(Σxy)/ n(Σx2) – (Σx)2

b = n (Σxy) – (Σx)(Σy) /n(Σx2) – (Σx)2

Y = a + bX1 + cX2 + dX3 + ∈

Where,

Y – Dependent variable

X1, X2, X3 – Independent (explanatory) variables

a – Intercept

b, c, d – Slopes

ϵ – Residual (error)

a = (((Σy) * (Σx2)) – ((Σx) * (Σxy))) / n * (Σx2) – (Σx)2

a = ((25 * 120) – (20 * 144)) / (4*120 – (20)2)

a = 1.5

b (Slope) is calculated using the formula given below

b = ((n * (Σxy)) – ((Σx) * (Σy))) / (n * (Σx2)) – (Σx)2

b = ((4 * 144) – (20 * 25)) / (4*120 – (20)2)

b = 0.95

So the regression line can be defined as Y = a +bX which is Y = 1.5 + 0.95 *