Question 1
Briefly and concisely discuss in your own words the following:

a. Explain the three characteristics of a correlation.
Answer:
1. The Direction of the Relationship. The correlation coefficient has a sign (plus or minus) and it shows the direction of the relationship (positive or negative).
2. The Form of the Relationship. The correlation coefficient uses for many forms of the relationship. The most common use of correlation is to measure straight-line relationships.
3. The Strength or Consistency of the Relationship. The correlation coefficient shows the consistency of the relationship. For a linear relationship, for example, each additional level of X, changes the value of Y by a consistent and predictable amount.

b. Describe an example of each of the four uses of correlation.
Answer:
Prediction: If two variables correlated, we can use the one variable to predict the other variable. For example, we expect that consumption and income are correlated. When income increases consumption also increases. So in order to predict consumption we can use income.
Validity: Scientist can be generate a new test for measuring language ability. For example, there suppose TOEFL and IELTS. In order to measure new language test validation, we can compute correlation coefficients for the results of all tests.
Reliability: If the reliability is high, the correlation coefficient must be strong. A model must give same results for same individuals in same situations. For example, you took 110 from TOEFLT test this week. If you take TOEFL in the next week, it is expected that you will get same (or nearly the same) score.
Theory Verification: In many sciences, there are many theories. For example, one scientist argue that there are strongly positive relationship btw mothers IQs and childâ€™s learning capability. It can be tests by the correlation coefficient.

Part A: Exploratory Data Analysis Preparation â€¢ Open the files...