Question

1.

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. X 5 14 13.31 13 13.66 12 13.74 10 13.05 9 12.30 4 4.31 6 8.34 8 11.25 11 13.54 7 9.94 y 6.46 = 3.00 + 0.80 (Round to two decimal places as needed.)

2.

3.

Answer 1

Question 1

ΣX = 99
ΣY = 119.9
ΣX * Y = 1178.1
ΣX2 = 1001
ΣY2 = 1412.6928

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 0.90
a =( Σ Y - ( b * Σ X) ) / n
a =( 119.9 - ( 0.9 * 99 ) ) / 11
a = 2.80
Equation of regression line becomes Ŷ = 2.80 + 0.90 X

Question 2

X :- Chest Size

Y :- Weight

ΣX = 316
ΣY = 2395
ΣX * Y = 128079
ΣX2 = 16806
ΣY2 = 980327

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 11.9
a =( Σ Y - ( b * Σ X) ) / n
a =( 2395 - ( 11.8918 * 316 ) ) / 6
a = -227.1
Equation of regression line becomes Ŷ = -227.1 + 11.9 X

When X = 50
Ŷ = -227.137 + 11.892 X
Ŷ = -227.137 + ( 11.892 * 50 )
Ŷ = 367.5

Question 3

X :- Chirps

Y :- Temperature

ΣX = 6366
ΣY = 499.2
ΣX * Y = 534834.9
ΣX2 = 6881548
ΣY2 = 41777.16

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 0.0407
a =( Σ Y - ( b * Σ X) ) / n
a =( 499.2 - ( 0.0407 * 6366 ) ) / 6
a = 39.97
Equation of regression line becomes Ŷ = 39.97 + 0.0407  X

b = (6+ 534834.9-6366 * 499.2)/(6+ 6881548 - (6366)