Question

This data set was downloaded from the site http://lib.stat.cmu.edu/DASL/ at Carnegie-Melon university. The original source is Willerman et al. (1991). The data consist of a sample of brain information recorded on 40 college students. The variables include gender, height, weight, three IQ measurements, and Magnetic Resonance Imaging (MRI) counts, as a determination of brain size. The data are in the rda file braindata. rda at the sites referenced in the Preface. For this exercise, consider the MRI counts. (a) Load the rda file braindata.rda and print the MRI data, using the code: \(\mathrm{mri}<-\) braindata \([, 7] ;\) print(mri). (b) Obtain a histogram of the data, hist \((m r i, p r=T)\). Comment on the shape. (c) Overlay the default density estimator, lines (density(mri)). Comment on the shape. 4.1.10. This data set was downloaded from the site http://lib.stat.cmu.edu/DASL/ at Carnegie-Melon university. The original source is Willerman et al. (1991). The data consist of a sample of brain information recorded on 40 college students. The variables include gender, height, weight, three IQ measurements, and Magnetic Resonance Imaging (MRI) counts, as a determination of brain size. The data are in the rda file braindata. rda at the sites referenced in the Preface. For this exercise, consider the MRI counts. (a) Load the rda file braindata.rda and print the MRI data, using the code: \(\mathrm{mri}<-\) braindata \([, 7] ;\) print(mri). (b) Obtain a histogram of the data, hist \((m r i, p r=T)\). Comment on the shape. (c) Overlay the default density estimator, lines (density(mri)). Comment on the shape.

Short answer

This exercise involves loading an rda file, extracting the MRI data, creating a histogram of said data, overlaying a density estimator, and then drawing conclusions about the data based on the produced visual. The results depend on the actual shape of the histogram and density line, implying the need for detailed visual examination to draw definitive conclusions.

Step-by-step solution

Loading and Printing the Data

Firstly, the R environment must be set up to run R scripts. Make sure that the 'braindata.rda' file is present in the correct directory. Now, load the 'braindata.rda' file and print the MRI data using the provided code: mri<- braindata[, 7]; print(mri). The 'mri' vector now contains the MRI counts.

Generating the Histogram

The hist() function is used to arrange data into grouped format for graphical representation. Generate a histogram of the MRI data with the probability density instead of the count on the y-axis by running: hist(mri, pr=T). Now, the shape of the data distribution can be visually inspected.

Overlaying the Density Estimator

After creating the histogram, overlay it with a default density estimator. Density estimation visualizes the probability density function of the underlying variable. To overlay the histogram with density estimator, use the lines() function: lines(density(mri)). Now, we have the histogram with a density line which gives a better understanding of the distribution.

Analyzing and Interpreting

Upon examining the histogram and overlaid density line, comments can be made about the shape of the data. These observations may reveal trends, patterns, or outliers in the brain data. The shape of the histogram might indicate the data to be normally distributed or skewed. Observations from this step will provide the final conclusion.