Question

We are studying the relationship of age in years and height in inches for children of ages from 2 - 10. We have a sample of five children. It is a linear relationship, so please find:

(a) r

(b) r(sq);

(c) the equation of the regression line

(d) the expected height in inches for a 7 year-old child.

Age(X)	Height(Y)
2	37
3	40
3	42
6	47
9	54

Answer 1

Here we have the relationship between the age and height of children where the age is expressed in years and height is expressed in inches, for children of ages 2-10.

Let x denote the age of children and y denote their height. Then the regression equation between the two variable is of the form

For obtaining the slope and the intercept, we minimize the residual sum of error given by

For minimizing the residual sum of error, we differentiate it with respect to A and B and we equate it to 0.This gives two normal equation which is given below

Therefore the paramter and slope of the equation is

Also the correlation coefficient r is given by

Therefore, for obtaining the correlation coefficient we need the mean of the variable which is given below

Now, we try to obtain to obtain the slope of the equation and the correlation coefficient, so consider the table below

Therefore the slope and intercept is

a) r=0.988

b) r(sq)=0.9761.

c) The regression equation is given by

Y=33.47+2.289*X

d) The expected height for 7 year old child is btined by putting X=7 in the above regression equation given by

Y=33.47+2.289*7=33.47+16.023=49.493.