Is brain size a measure of intelligence? Brain size tends to vary with body size: for example …

         Background: Is brain size a measure of intelligence? Brain   size tends to vary with body size: for example, sperm whales and elephants   have brains up to five times as massive as human brains. So across species,   brain size is not a perfect measure of intelligence. And within species, the   underlying organization (complexity of connections) and molecular activity of   the brain are likely to be more directly associated with intelligence than   mere size.               In this   assignment, we will investigate relationships between physiological measures   of the brain, and intelligence. Download and open the Excel   workbook, MHA610_Week 5_Assignment_Brain_Data.xls. The workbook contains   data on 20 youths, in rows two through 21. Eight variables (the columns) were   recorded on each individual; the column headings are given in row one. The   column headings are as follows:              IQ the individual’s IQ         Order the birth order (1 = firstborn, 2 =   not firstborn)       Pair marker for genotype         Sex gender, 1 = male, 2 = female         CCSA corpus callosum surface area (in   cm2)        HC head circumference (in cm)         TOTSA total brain surface area (in cm2)        TOTVOL total brain volume (in cm3)         WEIGHT body weight (in kg)                    The   neuroanatomical measures CCSA, TOTSA, and TOTVOL were determined from   magnetic resonance imaging (MRI) of the brains, followed by automated image   analyses of the scans. The corpus callosum is a bundle of neural fibers   beneath the cortex, connecting the left and right cerebral hemispheres of the   brain; it is the communication highway between the two hemispheres. (The more   lanes to the highway, the faster the traffic ought to flow.)              The   following questions can be answered in Excel, StatDisk, or other statistics   software you may have available.   (a) Examine   all of the pairwise correlations among the physiological measures CCSA, HC,   TOTSA, TOTVOL, and WEIGHT. Which two variables have   the strongest correlation? Report the correlation, and plot the   scattergram for these two variables. Also, report the correlation and plot   the scattergram for the two variables that have   the weakest correlation.              (b)   Determine whether the physiological parameters CCSA, HC, TOTSA, TOTVOL, and   WEIGHT are significant predictors of IQ. That is, run a sequence of   univariate regressions, with IQ as the dependent variable, and the   physiological parameters as the independent variables. Report the best   univariate regression with statistics and a graph of the regression. Describe   whether IQ can be accurately predicted from any of these brain measures   individually or in combination.              (c)   BONUS. Power law distributions, that is, functional relationships   between two variables in which one variable is roughly a power of the other,   are often used to model physiological data. One of the oldest power laws, the   square-cube law, was introduced by Galileo in the 1600’s: empirically, the   square-cube law states that as a shape grows in size, its volume grows faster   than its surface area. We shall investigate the square-cube law with two   variables from our dataset, CCSA and TOTVOL. If CCSA varies with some power   of TOTVOL, for example, CCSA = k * (TOTVOL) α (k is an unknown constant   here), then a simple way of estimating the exponent α is via linear   regression: take log(CCSA) as the dependent variable and log(TOTVOL) as the   independent variable; the fitted regression coefficient (slope) is an   estimate of the exponent. (Do you see why this is true?) Perform this linear   regression, and report your results. Describe whether the regression   coefficient is significantly different from 2/3. (The 2/3rd power law occurs   often in nature.)              IQ ORDER PAIR SEX CCSA HC TOTSA TOTVOL WEIGHT   96 1 1 2 6.08 54.7 1913.88 1005 57.607   89 2 1 2 5.73 54.2 1684.89 963 58.968   87 1 2 2 6.22 53 1902.36 1035 64.184   87 2 2 2 5.8 52.9 1860.24 1027 58.514   101 1 3 2 7.99 57.8 2264.25 1281 63.958   103 2 3 2 8.42 56.9 2216.4 1272 61.69   103 1 4 2 7.44 56.6 1866.99 1051 133.358   96 2 4 2 6.84 55.3 1850.64 1079 107.503   127 1 5 2 6.48 53.1 1743.04 1034 62.143   126 2 5 2 6.43 54.8 1709.3 1070 83.009   101 2 6 1 7.99 57.2 1689.6 1173 61.236   96 1 6 1 8.76 57.2 1806.31 1079 61.236   93 2 7 1 6.32 57.2 2136.37 1067 83.916   88 1 7 1 6.32 57.2 2018.92 1104 79.38   94 2 8 1 7.6 55.8 1966.81 1347 97.524   85 1 8 1 7.62 57.2 2154.67 1439 99.792   97 1 9 1 6.03 57.2 1767.56 1029 81.648   114 2 9 1 6.59 56.5 1827.92 1100 88.452   113 2 10 1 7.52 59.2 1773.83 1204 79.38   124 1 10 1 7.67 58.5 1971.63 1160 72.576