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.
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.
Consider the following: (a) Suppose you are given the following x, y data pairs. x 2...
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