Question

SHOW ALL WORK THROUGH MINITAB ONLY! Thank you! a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates (1,2), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b). 104TILL JOINT ott 0 2 4 6 8 10 Answer the following questions: 1. What is the equation of the regression line for all 10points? 2. What is the equation of the regression line for the set of 9points? Show transcribed image text

Answer 1

1.

Given 10 points are

Y	X
2	1
5	3
6	3
7	3
5	4
6	4
7	4
5	5
6	5
7	5

We will use R-software to find regression line for 10 point , any other software can be used , if manual calculation are required you can ask for that in comment box .

First we will import data into R

> x=scan("clipboard")
Read 10 items
> y=scan("clipboard")
Read 10 items

> x
[1] 1 3 3 3 4 4 4 5 5 5
> y
[1] 2 5 6 7 5 6 7 5 6 7

To verify our data we will plot it in R

> h1=seq(0,10,1)
> h2=seq(0,10,1)
> plot(h1,h2,"n",xlab="x",ylab="y")
> points(x,y,col="blue",pch=16)

| 0 24 68 10 246810

Hence our data is correct , now we will fit regression line for 10 points

> fit=lm(y~x)
> fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x
      2.766        0.766

Thus regression line for 10 points is

y = 2.766    +    0.766 * x

2. To fit regression line for 9 points , here we remove pair ( 1,2 )

Given 9 points are

Y	X
5	3
6	3
7	3
5	4
6	4
7	4
5	5
6	5
7	5

> x1=x[-1]
> x1
[1] 3 3 3 4 4 4 5 5 5
> y1=y[-1]
> y1
[1] 5 6 7 5 6 7 5 6 7

Hence our data is correct , now we will fit regression line for 10 points

> fit1=lm(y1~x1)
> fit1

Call:
lm(formula = y1 ~ x1)

Coefficients:
(Intercept)           x1
6.000e+00    2.658e-16

Thus regression line for 9 points is

y = 6.000e+00 + 2.658e-16 * x

To compare result from part a and b .

In part b ( i.e for 9 points ) we can observe estimate of b1 is 2.658e-16 , which is very small hence it concludes that there is no significance linear relation for 9 points , and all predicted mean response of y will be equal to 6 (b0), dosn't matter what value independent variable x takes

Where as in part a ( i.e for 10 points ) we can observe estimate of b1 is 0.766 , which states that all predicted mean response of y will depend on b0 as well as b1 , i.e there is some significance linear relation for 10 points .