Question

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

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

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

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

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

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

Do you get the least-squares equation of part (b) with the symbols x and y exchanged? 

Answer 1

a)

Sum of X = 9
Sum of Y = 14
Mean X = 3
Mean Y = 4.6667
Sum of squares (SS_X) = 14
Sum of products (SP) = 20

Regression Equation = ŷ = bX + a

b = SP/SS_X = 20/14 = 1.42857

a = M_Y - bM_X = 4.67 - (1.43*3) = 0.38095

ŷ = 1.429X + 0.381

b)

Sum of X = 14
Sum of Y = 9
Mean X = 4.6667
Mean Y = 3
Sum of squares (SS_X) = 28.6667
Sum of products (SP) = 20

Regression Equation = ŷ = bX + a

b = SP/SS_X = 20/28.67 = 0.69767

a = M_Y - bM_X = 3 - (0.7*4.67) = -0.25581

ŷ = 0.698X - 0.259

c) Yes, as you can see x value in part a is 1,2,6 and y values in part b is also 1,2,6 and same is for other data

d) ŷ = 1.429X + 0.381 . ( part a equation)

1.429x = y - 0.381

x = 0.699y - 0.267

e) No

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