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Suppose you are given the following (x, y) data pairs.x126y439Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x(b) Now suppose you are given these (x, y) data pairs.x439y126Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?YesNo    (d) Solve your answer from part (a) for x (rounded to three digits after the decimal).x =  +  y Do you get the least-squares equation of part (b) with the symbols x and yexchanged?YesNo    (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).In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.

Question

Suppose you are given the following (xy) data pairs.

x 1 2 6
y 4 3 9

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

(b) Now suppose you are given these (xy) data pairs.

x 4 3 9
y 1 2 6

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

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

YesNo    


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

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

YesNo    


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

In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.
check_circleAnswer
Step 1

(a)

Consider the given data and calculate the following:

Χ
ν
Χ
ν
1
1
16
2
3
6
4
9
6
9
54
36
81
ΣΧ9Σ) =16Σy, 64 ΣΧ41 ΣΕ106
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Χ ν Χ ν 1 1 16 2 3 6 4 9 6 9 54 36 81 ΣΧ9Σ) =16Σy, 64 ΣΧ41 ΣΕ106

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Step 2

Now, Least Squares Regression equation is given by:

Σw-(Σ) (Σ)
ηΣέ-Σ
3( 64)-(9) 16)
3(41)-(9)
192-144 48 1.14285714 1.143
123-81 42
=1.143
ΣΥ
bg
ΣΧ
--b
η
η
16
-(1.1431.904333 1.904
3
3
1.904
help_outline

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Σw-(Σ) (Σ) ηΣέ-Σ 3( 64)-(9) 16) 3(41)-(9) 192-144 48 1.14285714 1.143 123-81 42 =1.143 ΣΥ bg ΣΧ --b η η 16 -(1.1431.904333 1.904 3 3 1.904

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Step 3

Now, put the values b0 and b1 and the Least Squares Regression...

1.9041.143x|
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Image Transcriptionclose

1.9041.143x|

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