Question

Help please

The accompanying data on x = head circumference score (a comparison score with peers of the same age a positive care suggests a larger size than for peers) tape 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 ence Scores at SY 6-14 Months -0.71 690 1.7 700 720 740 1.5 750 750 760 780 790 1.6 1.6 3.3 820 825 835 2.85 (a) What is the value of the correlation coefficient? (Give the answer to two decimal places.) r=0.75 (b) Find the equation of the least squares line. (Give the answer to two decimal places)

Answer 1

(b)

From the given data, the following Table is calculated:

X	Y	XY	X2
-0.71	680	-482.5	0.5041
1.7	690	1173	2.89
-0.26	700	-182	0.0676
0.29	720	208.8	0.0841
0.34	740	251.6	0.1156
2.0	740	1480	4.0
1.6	750	1200	2.56
2.5	750	1875	6.25
1.6	760	1216	2.56
1.6	780	1248	2.56
2.5	790	1975	6.25
2.6	810	2106	6.76
3.3	815	2689.5	10.89
2.7	820	2214	7.29
0.94	825	775.5	0.8836
2.85	835	2379.75	8.1225
2.8	840	2352	7.84
2.7	845	2281.5	7.29
31.05	13890	24760.85	76.9175

AXOxΖ- D = ηΣΧ2 - (ΣΧ)2

(13890 x 76.9175) - (31.05 x 24760.85) 9) = 712.54 (18 x 76.9175) – 31.052

και ηΣΧΥ - ΣΧΣΥ ηΣ Χ2 – (Σ Χ)2

(18 x 24760.85) - (31.05 x 13890) (18 x 76.9175) – 31.052 = 34.28

So,

The equation of the least squares line is given by:

y = 712.54 + 34.28.

(c)

For x = 1.8, we get:

4 = 712.54+(34.28 x 1.8) = 774.24

So,

Answer is:

774.24