Answer to Question #282352 in Statistics and Probability for Bismark Akyen

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