Question

X value:1, 1, 1, 3, 3, 3, 3, 5, 5, 5 (months)

Y value: 4.7, 3.1, 4.0, 14.8, 13.4, 15.6, 14.2, 23.5, 22.2, 24.4 (kg)

1. Find the value of the linear correlation coefficient, write down the formula

2. Find the equation of the least squares regression line y = b0 + b1x

3. If a 4-month old puppy comes , what do you expect its weight?

4. If you record 2-months old puppy's weight by its residual value of -0.84kg, Find the puppy's acutual weight

Answer 1

1. Correlation Coeffcient formula:

n : number of observations(pairs)

n	10
x	30
y	139.9
xy	536.3
x2	114
y2	2531.75

Correlation Coeffcient = 0.992955

2.

Equation of the least squares regression line y = b0 + b1x

Formula :

b₁ = 4.8583

b_o = -0.5849

Equation of the least squares regression line y = -0.5849 + 4.8583x

3.

If a 4-month old puppy comes , what do you expect its weight

To get the predicted(expected) weight substitute age of the puppy : 4-month as 'x' in the  least squares regression line

i.e

(Predicted )Expected weight of 4-month old puppy = -0.5849 + 4.8583 x 4 = 18.8483

(Predicted )Expected weight of 4-month old puppy = 18.8483

4.

Residual = Actual value - predicted value;

i.e

Actual weight of 2-month old puppy = predicted weght of 2-month old puppy + Residual value recorded for 2-month old puppy's weight

Given residual of 2-month old puppy's weight= -0.84

Predicted weight of 2-month old puppy can be get by substituting x=2 in the least squares regression equation

Predicted weight of 2-month old puppy = -0.5849 + 4.8583 x 2 = 9.1317

Actual value = predicted value+ Residual = 9.1317 - 0.84 = 8.2917

puppy's actual weight for 2month old puppy = 8.2917