Question

The accompanying data on - head circumference z score (a comparison score with peers of the same age a positive score suggests a larger size than for peers) at age 6 to 14 months and y volume of cerebral grey matter (in ml) at age 2 to 5 years were read from a graph in an article Head Circumfere Cerebral Grey ence Scores at Matter (ml) 2-5 yr 6-14 Months 680 -0.75 1.2 700 -0.30 720 0.25 740 D.30 740 1.5 750 1.1 750 2.0 760 1.1 780 1.1 2.0 790 810 2.1 2.8 2.2 0.90 815 820 825 835 840 845 2.35 2.3 2.2 (a) What is the value of the correlation coefficient? (Give the answer to two decimal places.) (b) Find the equation of the least-squares line. (Give the answer to two decimal places.) 9 - (c) Predict the volume of cerebral grey matter for a child whose head circumference z score at age 12 months was 1.8. (Give the answer to two decimal places.)

Answer 1

Solution-:

Let, x= Head curcumference z-scoreat 6-14 montghs and y=Cerebral Grey Matter(ml) 2-5 year

By using R-Software:

> x=c(-0.75,1.2,-0.30,0.25,0.30,1.5,1.1,2.0,1.1,1.1,2.0,2.1,2.8,2.2,0.90,2.35,2.3,2.2);x
[1] -0.75 1.20 -0.30 0.25 0.30 1.50 1.10 2.00 1.10 1.10 2.00 2.10
[13] 2.80 2.20 0.90 2.35 2.30 2.20
> y=c(680,690,700,720,740,740,750,750,760,780,790,810,815,820,825,835,840,845);y
[1] 680 690 700 720 740 740 750 750 760 780 790 810 815 820 825 835 840 845
> #(a) for Correlation
> r=cor(x,y);r
[1] 0.786243
> round(r,2)
[1] 0.79
> # For regression line
> fit=lm(y~x);fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
714.15 42.52

> #The equation of the line of regression of y on x is:y=a+b*x
> #y=714.15+42.52*x
> #(c) When x=1.8
> esty=714.15+42.52*1.8;esty
[1] 790.686
> round(esty,2)
[1] 790.69

R-Code:

x=c(-0.75,1.2,-0.30,0.25,0.30,1.5,1.1,2.0,1.1,1.1,2.0,2.1,2.8,2.2,0.90,2.35,2.3,2.2);x
y=c(680,690,700,720,740,740,750,750,760,780,790,810,815,820,825,835,840,845);y
#(a) for Correlation
r=cor(x,y);r
round(r,2)
# For regression line
fit=lm(y~x);fit
#The equation of the line of regression of y on x is:y=a+b*x
#y=714.15+42.52*x
#(c) When x=1.8
esty=714.15+42.52*1.8;esty
round(esty,2)