Problem: In studying the effects of heredity and environment on intelligence, it has been helpful to analyze the IQ's of identical twins who separated soon after birth. Identical twins share identical genes inherited from the same fertilized egg. By studying identical twins raised apart, we can eliminate the variable of heredity and better isolate the effects of the environment. The first table shows the IQ's of pairs of identical twins (older twins are \(x\) ) raised apart.

The second table contains randomly generated numbers with the mean of 100 and standard deviation of 15, the same parameters as the standardized IQ test. The numbers simulate IQ's scores of 12 random pairs of siblings living in the same household ( $A$ is the older sibling).

1. Find the mean and standard deviations of the four distributions.
2. Use the measures in (a), the five measures of Exploratory Data Analysis, and Pearson Index to determine the shapes of the distributions.
3. Verify the shapes by analyzing histograms and boxplots of the distributions.
4. Check if there are any outliers and unusual values.
5. Compare the four distributions and try to find any associations between them.
6. Make a scatter diagrams of the of \(\mathrm{X}\) and \(\mathrm{Y}\), and later of \(\mathrm{A}\) and \(\mathrm{B}\). What conclusions can you draw from the diagrams?
7. Find a coefficient of correlation between \(X\) and \(Y\), and then between \(A\) and \(B\).
8. Determine the direction and strength of the correlations.
9. Find the equations of regression lines for the relationships between \(X\) and \(Y\), and A and B. Interpret the slopes and intercepts of the equations.

\(\mathrm{j}\). Find the coefficients of determination. Interpret their values.

k. Check if the linear model you used is correct for the associations (use the distributions of residuals).

1. Check if both correlations are significant for the size of the sample.

m. Write a summary statement about the effect of heredity and environment on intelligence and note that your conclusions are based on a small sample of 12.

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Solution: The downloadable solution consists of 20 pages, 1005 words and 28 charts.
Deliverable: Word Document