## Final Exam

December 5, 2013

Here is your Final Exam:

**1. **Analyze the exam data posted Dec 1^{st}, **Exam #3 Results** and complete the following.

- Use graphs to illustrate and characterize the relationships among exam scores.
- Calculate score averages and generate descriptive statistics for average scores.
- What is the probability that a randomly selected student has an average of 85% or higher?
- Produce a point estimate for the mean Final Exam score with a 95% confidence interval.
- Build a regression model to predict Final Exam scores and produce estimates.

**2. **Analyze historical monthly stock market prices for the S&P 500 Index (**data download: sp500history-monthly**) to answer the following.

- What is the relationship, if any, between trading volume and stock prices?
- Which decade was more volatile (higher stock price variability) – the 1990s or the 2000s?

**3. **Analyze the Monthly House Price Index data (**data download: MonthlyIndex_Jan1991_to_Latest**) to answer the following.

- Which region of the country has seen the highest increase in home prices?
- Which region of the country has had the most price variability?
- Which two regions are most closely correlated?
- Which region of the country is most closely correlated with the entire USA?

**4. **Use **data from problems #2 and #3** to answer the following.

- What is the relationship, if any, between housing prices and stock market prices?
- Can housing prices help predict stock market prices?
- Can stock market prices help predict housing prices?
- What is the difference between “correlation” and “causation” and how does it apply to this question?

**5. **Visit **http://fivethirtyeight.blogs.nytimes.com/** to read about **Nate Silver** and his statistical models for predicting the outcome of national elections.

- How would you go about producing a similar (yet simpler and easier to understand) type of model to predict the outcome of the 2014 Colorado Gubernatorial Election?
- Be specific about data you might gather, statistical techniques you think would be useful and how you would report your predictions to the public.

## 1 Comment

Two students have asked, “Should we just use Exam #3 results or all results?”. The short answer is “all results” but you will need to select and use the best set(s) of data to appropriately address each of the questions within #1. For example, the 3rd bullet, “What is the probability that a randomly selected student has an average of 85% or higher?” will most certainly require that you use all 3 sets of test scores in order to accurately calculate averages. On the other hand, the last bullet “Build a regression model to predict Final Exam scores and produce estimates” allows some flexibility in selecting data inputs for the model.