Question

(a) Suppose you are given the following (x, y) data pairs.

x	1	2	6
y	2	1	9

Find the least-squares equation for these data (rounded to three digits after the decimal).
? = ?+ ? x

(b) Now suppose you are given these (x, y) data pairs.

x	2	1	9
y	1	2	6

Find the least-squares equation for these data (rounded to three digits after the decimal).
? = ?+?  x

(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?

Yes or No    

(d) Solve your answer from part (a) for x (rounded to three digits after the decimal).
x = ?+ ? y

Answer 1

SolutionA:

Used R software:

x <- c(1,2,6)
y <- c(2,1,9)
rmod1=lm(y~x)
coefficients(rmod1)

output:

(Intercept) x
-0.7142857 1.5714286

least-squares equation for these data is

y=-0.714+1.571x

SolutionB:

x1 <- c(2,1,9)
y1 <- c(1,2,6)
rmod2=lm(y1~x1)
coefficients(rmod2)

output:

(Intercept) x1
0.6842105 0.5789474

the least-squares equation for these data

y=0.684+0.579x

Solutionc:

NO

Solutiond:

From (A)

y=-0.714+1.571x

1.571x=y+0.714

x=0.714/1.571+1/1.571y

x=0.454+0.637y