Question

Consider the following:

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

x	2	1	6
y	6	7	8

Find the least-squares equation for these data. (Use 3 decimal places.)

=

+  x

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

x	6	7	8
y	2	1	6

Find the least-squares equation for these data. (Use 3 decimal places.)

=

+  x

(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?
---Select--- Yes No

(d) Solve your answer from part (a) for x. (Use 3 decimal places.)

x =

+  y

Do you get the least-squares equation of part (b) with the symbols x and y exchanged?
---Select--- No Yes

(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs x, y. If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs y, x, (with x and y exchanged)? Explain using parts (a) through (d).

Switching x and y values will not necessarily produce the same least-squares equation every time.Switching x and y values will never produce the same least-squares equation every time.    Switching x and y values will produce the same least-squares equation every time.

Answer 1

a.

Sum of X = 9
Sum of Y = 21
Mean X = 3
Mean Y = 7
Sum of squares (SSX) = 14
Sum of products (SP) = 4

Regression Equation = ŷ = bX + a

b = SP/SSX = 4/14 = 0.286

a = MY - bMX = 7 - (0.29*3) = 6.143

ŷ = 0.286X + 6.143

b.

Sum of X = 21
Sum of Y = 9
Mean X = 7
Mean Y = 3
Sum of squares (SSX) = 2
Sum of products (SP) = 4

Regression Equation = ŷ = bX + a

b = SP/SSX = 4/2 = 2

a = MY - bMX = 3 - (2*7) = -11

ŷ = 2X - 11

c. Yes

d. Sum of X = 21
Sum of Y = 9
Mean X = 7
Mean Y = 3

Sum of squares (SSy) = 14
Sum of products (SP) = 4

X= 0.286Y + 6.143

e. Switching x and y values will not necessarily produce the same least-squares equation every time.