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.

Cerebral Grey Matter (ml) 2-5 yr	Head Circumfer- ence z Scores at 6-14 Months
680	-0.72
690	1.6
700	-0.27
720	0.28
740	0.33
740	1.9
750	1.5
750	2.4
760	1.5
780	1.5
790	2.4
810	2.5
815	3.2
820	2.6
825	0.93
835	2.75
840	2.7
845	2.6

(a) What is the value of the correlation coefficient? (Give the answer to two decimal places.)
r =


(b) Find the equation of the least-squares line. (Give the answer to two decimal places.)
=

(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

EXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter Head Circumfer-z Scores at 6-14 Months in one column and enter Cerebral Grey Matter 2-5 yrence in one column. Step 2: In Data, select Data Analysis and choose Regression. Step 3: In Input Variable Y Range: select Cerebral Grey Matter 2-5 yrence. Step 4: In Input Variable X Range: select Head Circumfer-z Scores at 6-14 Months. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.755733 0.571132 0.544327 36.22249 18 ANOVA df 1 Regression Residual Total SS MS F gnificance F 27956.9 27956.9 21.30749 0.000286 20993.1 1312.069 48950 16 17 Coefficientandard Err t Stat P-value Lower 95%Upper 95% Intercept 712.7687 15.35246 46.42702 1.71E-18 680.223 745.3145 Head Circumfer-z Scores at 6-14 Months 35.69573 7.733038 4.616003 0.000286 19.30242 52.08904 The value of the correlation coefficient is r=0.76. (6) The equation of the least-squares line is = 712.77+35.70 x.

(c) û = 712.77 +35.70 x =712.77 +35.70(1.8) = 712.77 +64.26 = 777.03

Thus the best predicted volume of cerebral grey matter for a child whose head circumference z score at age 12 months was 1.8 is 777.03.