Testing Method

1. Linear Regression of Brain Measurements on IQPattrick Bennett, Madelyn KellyThe Wallace H. Coulter Department of Biomedical Engineering (1),Georgia Institute of Technology/Emory University, Atlanta, GA, USA Introduction Identical twins share numerous traits. Advances in vivo brain image aquirement and analysis has made it possible to determine if monozygotic twins share neuroanatomical traits and if these measures correlate with brain size. Using magnetic resonance imaging and computer based image techniques Therese Sukele1 collected measurements of corpus collasum (CCSA), surface area (TA) and forebrain volume (TV). Body weight, head circumference (HC) and IQ were also measured. Analysis of variance were carried out using birth order (O) and sex (S). We are going to use these numbers to test for linear relationship between the brain measurement variables and IQ by linear regression and test for correlation between brain measurements. Minitab Predictor Coef SE Coef T P Constant 75.1 116.0 0.65 0.529 ccsa2 3.288 5.568 0.59 0.565 headcir3 1.192 2.414 0.49 0.630 totsa4 -0.02911 0.02536 -1.15 0.272 totvol5 -0.00648 0.04473 -0.14 0.887 bw6 -0.0154 0.1755 -0.09 0.931 bo -0.009 6.870 -0.00 0.999 Analysis of Variance Source DF SS MS F P Regression 6 578.5 96.4 0.46 0.827 Residual Error 13 2737.5 210.6 Total 19 3316.0 Correlation CCSA2 IQ HC3 O7 P8 S9 TA4 TV5 IQ 0.156 0.511 HC 0.613 0.138 0.004 0.562 O -0.077 0.047 -0.070 0.747 0.845 0.769 P 0.269 0.333 0.681 0.000 0.251 0.152 0.001 1.000 S -0.280 0.039 -0.671 0.000 -0.870 0.232 0.871 0.001 1.000 0.000 TA 0.337 -0.291 0.337 -0.204 -0.015 -0.030 0.146 0.213 0.147 0.389 0.951 0.901 TV 0.662 -0.063 0.508 0.035 0.391 -0.363 0.601 0.001 0.791 0.022 0.884 0.088 0.115 0.005 BW6 0.082 -0.003 0.240 0.011 0.336 -0.139 0.064 0.208 0.732 0.991 0.308 0.963 0.148 0.560 0.788 0.379 Results & Conclusion The regression equation is iq = 75 + 3.29 ccsa + 1.19 headcir - 0.0291 totsa - 0.0065 totvol - 0.015 bw The resdiual plot for IQ proves this is a good regression model. As you can see from the Minitab results the p-values for all of the variables are greater than 5%. Therefore our null hypothesis can not be rejected. This proves there is not a significant linear relationship between these brain measurements and the child’s IQ. However from the correlation data there is a relationship between the different brain measurements which is to be expected. Monozygotic twins share similarities in forebrain volume and corpus collasum surface. Testing Method The null hypothesis (H0: β = 0) for each of the columns was tested versus the alternative hypothesis (H1: β ≠ 0) where β is the underlying slope of the regression line. The objective is to determine if there is a significant linear relationship between each of these measurements and the child’s IQ. Minitab was used to perform a regression test. The correlation between all of the variables was also determined. References [1] Therese Stukel of Dartmouth Hitchcock Medical Ceter http://lib.stat.cmu.edu/datasets/IQ_Brain_Size 2 - Corpus Collasum Surface Area (cm) 3 - Head Circumference (cm) 4 - Surface Area of Cerebral Cortex (cm2) 5 - Volume of Forebrain (cm3) 6 - Body Weight (kg) 7 - Order Born (1/2) 8 - Pairs 9 - Sex