1. Compute the average elevation, minimum elevation, maximum elevation, range of elevation (4 points).
2. Determine the top 3 zip codes in the country according to Per_capita_income. Where are they located? Just type the zip code into Google. (3 points)
3. Which zip code is at the 25th percentile for percentage of the population that is female and 75 or older? Where is it? (2 points)
4. What is the correlation coefficient between the average annual minimum temperature and the average annual snowfall? (2 points)
5. Compute the sum of Pct_farm, pct_non_farm, pct_urban for each zip code. Suppose you are going to build a linear regression model using these three variables as input variables, what does this tell you? (2 points)
6. State the type of variable and give an explanation: zip code, per_capita_income, avg_annual_temp_max. (3 points)
7. Compute the correlation coefficient between the average annual maximum temperature and the average annual number of heating degree days. (2 points).
8. Build a linear regression model to compute the number of heating degree days given the average annual maximum temperature. (10 points)
   1. Show the scatterplot.
   2. Calculate the estimate b1.
   3. Calculate the estimate b0.
   4. Calculate the 95% confidence interval for b ₁ .
   5. Calculate the 95% confidence interval for b ₀ .
   6. With 95% level of confidence, is b ₀ different from 0? Explain your answer.
   7. With 95% level of confidence, is b ₁ different from 0? Explain your answer.
   8. Calculate the fitted values of y and plot this line on the scatterplot.
   9. Calculate R ² .
9. The selling price of a used car is inversely (or negatively) related to the age of the car. That if the age increases, the selling price tends to decrease. The following table shows data for 10 cases of a certain make and model:

1. Plot the data.
2. Find the equation of the sample regression line and graph it.
3. Estimate the selling price of a 4-year-old car.

10. Exercise 15.S.20 (5 points)

An agent for the Internal Revenue Service claims that there is a linear relationship between people’s wage income (X) and their income earned from interests and dividend (Y).

1. Use the accompanying data and find the sample regression line that expresses \(Y\) as a linear function of \(X\).
2. Plot the data on a scatter diagram.
3. Find \(R^{2}\). Based on this value of \(R^{2}\), would you feel confident in predicting the interest and dividend income of a household with a wage income of $35,000?
4. Let \(\alpha=.05\). Test the null hypothesis that wage income does not help explain interest and dividend income.
   11. Suppose that X is normally distributed with mean = 22 and variance = 16. (2 points)
   1. Compute P(21 ≤ X ≤ 25).
   2. Compute P(X > 30).

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