Question

The accompanying data are the length​ (in centimeters) and girths​ (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not.

​(a) x=140 cm

​(b) x=172 cm

​(c) x=164 cm

​(d) x=158 cm

Length, x= 138 168 151 144 160 160 124 136 154 148 148 147            

Girth, y= 107 131 116 107 125 118 104 103 120 111 106 108

1. Find the regression equation.

2. Graph below

Answer 1

ΣX =  1778 ΣY = 1356 ΣX * Y = 201954    ΣX2 = 265010   ΣY2 = 154110

Equation of regression line is Ŷ = a + bX


b = 0.663
a =( Σ Y - ( b * Σ X) ) / n
a =( 1356 - ( 0.6626 * 1778 ) ) / 12
a = 14.831
Equation of regression line becomes Ŷ = 14.8305 + 0.6626 X

When X = 140
Ŷ = 14.831 + 0.663 X
Ŷ = 14.831 + ( 0.663 * 140 )
Ŷ = 107.65

When X = 172
Ŷ = 14.831 + 0.663 X
Ŷ = 14.831 + ( 0.663 * 172 )
Ŷ = 128.87

When X = 164
Ŷ = 14.831 + 0.663 X
Ŷ = 14.831 + ( 0.663 * 164 )
Ŷ = 123.56

When X = 158
Ŷ = 14.831 + 0.663 X
Ŷ = 14.831 + ( 0.663 * 158 )
Ŷ = 119.58