Answer to Question #194980 in Statistics and Probability for Muhammad Abid

Question #194980

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).

 


1
Expert's answer
2021-05-20T14:46:54-0400



Xˉ=Xn=748=9.25Yˉ=Yn=4158=51.875\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-


byx=nXYXYnX2(X)2b_{yx}=\dfrac{n\sum XY-\sum X \sum Y}{n\sum X^2-(\sum X)^2}


=8(3903)(74)(415)8(722)(74)2=30.735300=0.10245=\dfrac{8(3903)-(74)(415)}{8(722)-(74)^2}\\[9pt]=\dfrac{30.735}{300}=0.10245


Regression equation of yon x is-


yyˉ=byx(xxˉ)y51.875=0.10245(x9.25)y=0.10245x+50.927y-\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=52.46x=15, y=0.10245(15)+50.927=52.46


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