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 are in the file IQBrain.csv. 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.
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 |
(a) Obtain the following R output, treating IQ as the response variable:
(i) scatter plot [3]
(ii) standardised residual plot [2]
(iii) distributionofresiduals [3] (iv) regressionanalysis(summaryoflinearmodel). [2,total=10]
(b) What statistical model is assumed in your regression analysis?
[2]
(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]
(e) Provide a 95% prediction interval for the verbal IQ of a female whose brain volume was 870,000 pixels. [4]
(f) One of the students showed the scatterplot to a friend who said, “Well, there is clearly a trend there. It looks like people with larger brains do have higher IQ.” Write a brief response to this comment.
a)
i) Read data into R as follows and run plot command:
> data = read.csv("input.csv") //assuming data is in input.csv file
> plot(x=data$BrainV, y=data$IQ)
Carrying out regression analysis in R:
> model = lm(data$IQ ~ data$BrainV)
> summary(model)
Call:
lm(formula = data$IQ ~ data$BrainV)
Residuals:
Min 1Q Median 3Q Max
-38.718 -18.870 9.529 16.373 27.069
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.18350 76.38158 0.317 0.755
data$BrainV 0.09884 0.08837 1.119 0.278
Residual standard error: 21.53 on 18 degrees of freedom
Multiple R-squared: 0.06499, Adjusted R-squared:
0.01305
F-statistic: 1.251 on 1 and 18 DF, p-value: 0.278
ii) Plot of std residuals:
> plot(model$residuals)
iii) The residuals look evenly distributed around a central mean line.
iv) Summary of the regression analysis is shown before answer ii) above
b) Least squares regression analysis is the model used above
c) The high p-value of 0.278 of the coefficient of the predictor variable BrainV shows that the model is not quite appropriate for the data
d) As p-value of coefficient of the predictor variable BrainV > 0.05, it is not a significant predictor of IQ at the 5% significance level.
e) 95% prediction interval is given by:
where = 0.09884 * 870 + 24.18350 = 110.1743
and tn-2, (1-alpha/2) = t-score (two-tailed) for n-2 = 18 dof at 5% significance level = 2.101
Hence, PI = (63.5, 156.85)
f) The IQ seems higher at some lower as well as higher end of the brain sizes. Hence, there doesn't seem to be a clear increasing trend in IQ levels as Brain size increases. Hence, the comment is invalid.
Some female psychology students were investigating whether intelligence depends on brain size. They each took a standard...
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...
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, file named IQBrain.csv. 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...
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, file named IQBrain.csv. 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...
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 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...
answer that i can understand well please Question 4 5 points Save Answer Researchers wondered whether the size of a person's brain was related to the individual's mental capacity They selected a sample of right-handed Anglo introdu psychology students who had Scholastic Aptitude Test scores higher than 1350. The subjects were administered the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. The MRI scans, performed at the same facility, consisted of 18 horizontal MR images. The comp of the...