Question

The following data represents the amount in kg of fertilizer applied to equal size of plots and the yields in kg of maize.

PLOT

AMOUNT OF FERTILIZER(X)

YIELDS(Y)

A

2

7

B

1

3

C

3

8

D

4

10

 

(a)   Calculate and interpret the correlation coefficient for X and Y               6 marks

 

(b)  Calculate and interpret the least square regression of Y on X                 8 marks

 

Answer 1

a)

correlation coefficient:

$r =\frac{ Σ(x_i - x̄)(y_i - ȳ)}{\sqrt{(Σ(x_i - x̄)^2Σ(y_i - ȳ)^2 )}}=0.9648$

there is a significant large positive relationship between X and Y

b)

regression line:

$y=b_1x+b_0$

where

$b_1=\frac{Σ(x_i-x̄)(y_i-ȳ)}{Σ(x_i-x̄)^2}=2.2$

$b_0 = ȳ - b_1x̄=1.5$

slope of line b₁ is rate of change of yields (Y) respect to amount of fertilizer (X)

b₀ is value of yields for amount of fertilizer = 0