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The best prediction of the player's weight using a line of best fit if 70 inches tall joins the team is x = 70 and y = 743.21.
What is line of best fit?
Assume y = a +bx as a line of best fit(trend line). Using the principle of least squares we can determine the parameters 'a' and 'b'.
According to the question,
Let y = a+ bx be the line of best fit. We have to determine the best prediction of the player's weight using a line of best fit if 70 inches tall joins the team.
Heights of the players weights X Y X² XY
(x) (y)
60 100 -8 32 64 256
62 120 -6 52 36 312
64 130 -4 62 16 248
66 140 -2 72 4 144
68 150 0 82 0 0
70 160 2 92 4 184
72 170 4 102 16 408
74 180 6 112 36 672
76 190 8 122 64 976
78 200 10 132 100 1320
Let X = x-68; Y= y-68; ∑X =10 ; ∑Y= 1850 ; ∑XY= 4520; ∑X² = 340;
∑x = 690;∑y=1540.
The normal equations are,
n a + b ∑X = ∑Y
a ∑X + b ∑X² = ∑XY
10a+10b = 1850 →(1)
10a + 340b = 4520 →(2)
Subtracting (1) from (2)
-330b = -2670
b = 8.09
Substituting b=8.09 in equation (1) we get,
10a + 10(8.09) = 1850
10a + 80.9 = 1850
10a = 1850 - 80.9
10a=1769.1
a=1769.1/10
a=176.91
The line of best fit is y = 176.91 + 8.09x
To determine the best prediction of the player's weight using a line of fit if 70 inches tall joins the team.
Put x = 70inches in the line of best fit.
y = 176.91 + 8.09(70)
y = 743.21
Hence, the best prediction of the player's weight using a line of best fit if 70 inches tall joins the team is x = 70 and y = 743.21
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