Question

The accompanying data on x = 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 Circumfer- Cerebral Grey Matter (ml) 2-5 yr 6-14 Months ence z Scores at 680 -0.72 690 1.4 700 -0.27 720 0.28 740 0.33 740 1.7 750 1.3 750 2.2 760 1.3 780 1.3 790 2.2 810 2.3 815 3.0 820 2.4 825 0.93 835 2.55 840 2.5 845 2.4 (a) What is the value of the correlation coefficient? (Give the answer to two decimal places.) r = 712.11 x (b) Find the equation of the least-squares line. (Give the answer to two decimal places.) ŷ = 43.57 (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.) 790.55 X

Answer 1

Solution

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable.

Select Input X Range as Range of independent variable

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.77
R Square	0.60
Adjusted R Square	0.57
Standard Error	35.16
Observations	18.00
ANOVA
	df	SS	MS	F	Significance F
Regression	1.00	29166.90	29166.90	23.59	0.00
Residual	16.00	19783.10	1236.44
Total	17.00	48950.00
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	712.69	14.70	48.47	0.00	681.52	743.85	681.52	743.85
Head Circumference	39.17	8.07	4.86	0.00	22.08	56.27	22.08	56.27

a) correlation r = 0.77

b) y=712.69+39.17*Head Circumference

c)

Head Circumference = 1.8

y=712.69+39.17*Head Circumference

y=712.69+39.17*1.8

y = 783.10