Question

A social researcher wants to determine if there is any association between the age in years and height in inches. A random sample of 8 students from a school was taken and their ages and heights were recorded as follows:

Age

6

7

8

8

10

11

12

12

Height

46

47

50

51

54

54

56

57

Find the linear regression equation and compute the height of student (Y) who will be 15 years of age (X=15).

 

Answer 1

$\bar{X}=\dfrac{\sum X}{n}=\dfrac{74}{8}=9.25 \\[9pt] \bar{Y}=\dfrac{\sum Y}{n}=\dfrac{415}{8}=51.875$

Regression coefficient of Y on X-

$b_{yx}=\dfrac{n\sum XY-\sum X \sum Y}{n\sum X^2-(\sum X)^2}$

$=\dfrac{8(3903)-(74)(415)}{8(722)-(74)^2}\\[9pt]=\dfrac{30.735}{300}=0.10245$

Regression equation of yon x is-

$y-\bar{y}=b_{yx}(x-\bar{x}) \\[9pt] \Rightarrow y-51.875=0.10245(x-9.25) \\[9pt] \Rightarrow y=0.10245x+50.927$

So At $x=15, y=0.10245(15)+50.927=52.46$