Question

Complete parts​ (a) through​ (h) for the data below.

x- 40, 50, 60, 70, 80

y-62, 58, 55, 47, 33

B) Find the equation of the line containing the points (50, 58) and (80, 33)

y=__x+(__)

D) By hand, determine the least-squares regression line

The equation of the​ least-squares regression line is given by

ModifyingAbove y with caret equals b 1 x plus b 0y=b1x+b0

where b1 equals r times StartFraction s Subscript y Over s Subscript x EndFractionb1=r•sysx

is the slope of the​ least-squares regression line and

b 0 equals y overbar minus b 1 x overbarb0=y−b1x

is the​ y-intercept of the​ least-squares regression line.

First find the correlation​ coefficient, r.

(f) Compute the sum of the squared residuals for the line found in part​ (b).

The residual is given by the formula below.

Residual=observed y−predicted y=y−y^

(g) Compute the sum of the squared residuals for the​ least-squares regression line found in part​(d).

The residual is given by the formula below.

Residual=observed y−predicted y=y−ModifyingAbove y with caret

Answer 1

Solution:-)

A) The equation of line passes through two points, (50,58) and (80,33).

y=mx+b, slope is given by

Therefore, we have

The equation of the line will be ,

We have computed the following calculations in R code, where on R.H.S. is output and on L.H.S is R code .

D) The equation of the​ least-squares regression line is given by

E) The correlation​ coefficient, r =  -0.9513848

(F) The sum of the squared residuals for the line is given by 63.12564

G) The residual is given by the formula below.

Residual=observed y−predicted

-2.8 ,0.1, 4.0, 2.9, -4.2

(g)The sum of the squared residuals for the line is given by  13481.1.