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Question: The age and height of a person is recorded. Determine the equation of the regression line.| Age (years) (x) | 16 | 18 | 21 | 24 | 28 | 33 | 40 | | Height (feet) (y) | 5 | 5.1 | 5.3 | 5.55 | 5.6 | 5.6 | 5.6 |
A ) y′ = 4.74 + 0.03x
B ) y′ = - 4.74 - 0.03x
C ) y′ = - 4.74 + 0.03x
D ) y′ = 4.74 - 0.03x
Steps to derive
1 Make a table with values for x, y, x2, xy
2 Regression line equation is y′ = a + bx
a = (Σy)(Σx2)-(Σx)(Σxy)n(Σx2)-(Σx)2
b = n(Σxy)-(Σx)(Σy)n(Σx2)-(Σx)2
3 a = 4.74, b = 0.03
[Substitute the values and simplify.]
4 Therefore, the equation of the regression line y′ = a + bx is y′ = 4.74 + 0.03x.
Hence the right answer is Option A
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