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Question
The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:
| X | 61 | 68 | 68 | 64 | 65 | 70 | 63 | 62 | 64 | 67 |
| Y | 112 | 123 | 130 | 115 | 110 | 125 | 100 | 113 | 116 | 125 |
Estimate weight of the student of a height 69 inches.
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Solution
| Height (X) |
Weight (Y) |
dx = X − 65 | dy = Y − 117 | dx2 | dy2 | dxdy |
| 61 | 112 | − 4 | − 5 | 16 | 25 | 20 |
| 68 | 123 | 3 | 6 | 9 | 36 | 18 |
| 68 | 130 | 3 | 13 | 9 | 169 | 39 |
| 64 | 115 | − 1 | − 2 | 1 | 4 | 2 |
| 65 | 110 | 0 | − 7 | 0 | 49 | 0 |
| 70 | 125 | 5 | 8 | 25 | 64 | 40 |
| 63 | 100 | − 2 | − 17 | 4 | 289 | 34 |
| 62 | 113 | − 3 | − 4 | 9 | 16 | 12 |
| 64 | 116 | − 1 | − 1 | 1 | 1 | 1 |
| 67 | 125 | 2 | 8 | 4 | 64 | 16 |
| 652 | 1169 | 2 | − 1 | 78 | 717 | 182 |
N = 10, ∑X = 652, ∑Y = 1169, ∑dx = 2, ∑dy = − 1, ∑dx2 = 78, ∑dy2 = 717, ∑dxdy = 182, `bar"X" = 652/10` = 65.2, `bar"Y" = 1169/10` = 116.9
byx = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`
= `(10(182) - (2)(-1))/(10(78) - (2)^2)`
= `1822/776`
= 2.3479
Regression equation of Y on X
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 117 = 2.3479 (X – 65.2)
Y – 117 = 2.3479X – (2.3479)(65.2)
Y = 2.3479X – 153.08308 + 117
Y = 2.3479 – 36.08308
When the height X = 69 inches
Weight, Y = 2.3479(69) – 36.08308
= 162.0051 – 36.08308
= 125.92202
= 125.92 lb
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