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 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.

Whether intelligence depends on brain size 950 900 850 800 130 120 100 110 90 30) 70 IC.)

(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. [2]

Answer 1

e)

Note that IQ is dependent variable

and Brain Volume is independent variable

data <- read.csv("../Documents/brainIq.csv")
BrainV <- data[,2]
IQ <- data[,1]
model <- lm(IQ ~ BrainV)
summary(model)
predict(model,data.frame(BrainV = 870),interval="interval")

summary(model) Call: lm(formula = IQ ~ 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 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 > predict(model,data.frame(BrainV = 870),interval="prediction") fit lwr upr 1 110.176 63.80803 156.544

>

hence 95% prediction interval is (63.808,156.544)

f) This statement is not correct

correlation does not imply causation