Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# 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: - Business Mathematics and Statistics

Sum

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.

#### 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

Concept: Regression Analysis
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