# 3. [25 marks] Some female psychology students were investigating whether intelligence depends on brain size. They each t...

###### Question:

3. [25 marks] Some female psychology students were investigating whether intelligence depends on brain size. They each took a standard test that measured verbal IQ and also underwent an MRI scan to measure their brain size. The resulting data is below.

 IQ BrainV 132 816.932 132 951.545 90 928.799 136 991.305 90 854.258 129 833.868 120 856.472 100 878.897 71 865.363 132 852.244 112 808.02 129 790.619 86 831.772 90 798.612 83 793.549 126 866.662 126 857.782 90 834.344 129 948.066 86 893.983

The variables are:

IQ Result of the verbal IQ test. IQ is measured on an artificial index scale, usually meant to have an average value of 100.

BrainV Brain volume measured in thousands of ‘pixels’. The size of a pixel derives from the two-dimensional resolution of the MRI and the spacing of image ‘slices’. It can vary between scanners (and even between scans on the same scanner). The pixel size is the same for all scans in this study, but the standard volumetric equivalent (e.g., millilitres) is not known.

(c) As far as possible, assess the extent to which the model is appropriate to the data. [4]

(d) Leaving aside any problems identified in part (c), evaluate the evidence that verbal IQ is related to brain volume. Use a 5% significance level, and describe any relationship you find. [3]

Whether intelligence depends on brain size 130 o 120 110 E 100 90 80 70 800 850 900 950 BrainV (ml)
Whether intelligence depends on brain size (0D 2 70 80 90 100 110 120 130 BrainV (ml)
Distribution of Standardised Residuals 2 2.0 1.5 1.0-0.5 0.0 0.5 1.0 1.5 Standardised residual