Statistics Regarding ACT Composite Score and SAT Total Score - Statistics Assignment Help

Assignment Task

1. In Section 1, what kind of relationship can be inferred from summary statistics regarding ACT composite score and SAT total score? Which visualisations make this relationship apparent?

2. Based on the box plots presented in Section 1, what is the relationship between parental level of education and parental income? Using table visualisation, find and show the entire rows that correspond to the outliers regarding parental income whose parents have a master's degree.

3. Using an example, explain the importance of scaling features so that their magnitudes are comparable when computing distances.

4. In Section 1, the distance matrix visualisation is not very informative. However, it is still possible to infer that the average distance between students whose parents only have some high school education and students whose parents have a master's degree is larger than the average distance between students whose parents only have some high school education. Explain how this inference is possible from the visualisation.

5. In Section 2, increase the number of evenly spaced numbers from 10 to 100 for both axes and observe the corresponding heat map created through nearest neighbour interpolation. Read about this interpolation method and explain what you observed.

6. The function load_wine from sklearn.datasets can be used to load the wine dataset into a DataFrame by using the commands data = load_wine(), df = pd.DataFrame(data.data, columns=data.feature_names), and df['target'] = pd.Series(data.target).

6.1. Load the wine dataset. Compute the frequency of each value of the 'target' feature.

6.2. Compute univariate and multivariate summaries for all numerical features (except from the target feature). Group observations by the target feature and compute the corresponding median for each numerical feature.

6.3. Group observations by the target feature and create one box plot of alcohol for each group.

6.4. Create a scatter plot for the pair of distinct numerical features with the highest correlation.

6.5. Exclude the target feature, standardize the remaining numerical features, and display a projection obtained by multidimensional scaling. Color the points by the target feature.

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