Question
Asked Oct 18, 2019

Considering the data types below compute a and b for Y = a + bX and the value for R-Squared. Show all work

X Y
1 2
2 1
3 4
4 8
5 11
6 11
7 12
8 21
check_circleExpert Solution
Step 1

The provided data table is:

xy
X
2
1
4
2
2
4
1
2
4
9
16
12
4
8
16
64
32
11
5
25
121
55
6
11
36
121
66
12
7
49
144
84
8
21
64
441
168
Σx=36 Σν= 70
y2912
xy = 421
Σ
=204
N
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xy X 2 1 4 2 2 4 1 2 4 9 16 12 4 8 16 64 32 11 5 25 121 55 6 11 36 121 66 12 7 49 144 84 8 21 64 441 168 Σx=36 Σν= 70 y2912 xy = 421 Σ =204 N

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Step 2

The required values are calculated below:

Σν
Σ
п
36
70
8
8
4.5
8.75
7
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Σν Σ п 36 70 8 8 4.5 8.75 7

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Step 3

The values of ‘a’ and ‘b&rs...

ηΣw-(Σ3)(Σ)
"Σέ-(Σε)
8(421)-(36)(70)
8(204)-(36)
=9
2.5238
a -bx
=8.75-2.5238 x 4.5
-2.6071
Thus, the equation of the least squares line is,
yabx
j-2.60712.5238.x
help_outline

Image Transcriptionclose

ηΣw-(Σ3)(Σ) "Σέ-(Σε) 8(421)-(36)(70) 8(204)-(36) =9 2.5238 a -bx =8.75-2.5238 x 4.5 -2.6071 Thus, the equation of the least squares line is, yabx j-2.60712.5238.x

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