Question

Listed below are the IQ scores of identical twins that were adopted and raised apart. One Twin Other Twin 90 95 99 101 105 106 109 103 111 113 98 100 89 92 115 116 100 102 107 104 110 112 102 101 98 99 92 94 100 101 111 112 117 120 102 99 95 93 105 107

Predict the IQ of the 2nd twin if the IQ of the 1st twin was 118.

Round your answer to 3 decimal places.

Answer 1

Solution:

Here, we have to predict the IQ score of the second twin if the IQ score of the first twin was 118.

First of all we have to find the regression equation for the prediction of the IQ score of the second twin. The regression output by using Excel data analysis is given as below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.94806221
R Square	0.898821953
Adjusted R Square	0.893200951
Standard Error	2.554600556
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1043.532288	1043.532	159.9042	2.16172E-10
Residual	18	117.467712	6.525984
Total	19	1161
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8.148339179	7.562073884	1.077527	0.295474	-7.738988488	24.03566685
First twin	0.927996699	0.073386553	12.64532	2.16E-10	0.773817273	1.082176125

From above regression output, the regression equation for the prediction of IQ score of second twin is given as below:

Y = 8.1483 + 0.9280*X

IQ of second twin = 8.148339179 + 0.927996699*IQ of first twin

We are given

IQ of first twin = 118

IQ of second twin = 8.1483 + 0.9280*118

IQ of second twin = 117.652

Predicted IQ score of second twin = 117.652