Problem 1

Somewhere in the Milky Way Galaxy, a class of 2,000 students took a course in Astronomy.  The first exam scores and the final exam percentage reached earth, but transmission broke off after only a dozen students' scores were received.  This is the only information available about that class.  That information is in the table below.

Use these data to answer the following questions

1. Using a pencil, paper, and a calculator, find the slope and the intercept term for
   Final = a + b Exam1.  Show your work, step by step.
2. Calculate the regression.  Show numbers as two decimal places even if you get 0.00.  Print out the Excel results and include them with your homework.

Problem 2

Suppose you are trying to explain why different white men have different levels of earnings.  You find the following regression results for a sample of 36,836 white men between the ages of 18 and 93:

EARNS = - 34,164.8 + 477.6 EXPER + 5,792.0 EDUC
                   (-32.4)        (28.8)                (68.9)

where

EARNS is the total salary and wages earned by the individual in 2000,

EXPER is an approximation of the person's work experience, calculated as the person's age minus 5 minus EDUC

EDUC is the number of years the person attended school

The numbers below the coefficients are t-statistics

R² = - 0.12, F-statistic is 2,547.8.  The standard error of the regression is 3,753.2.

Use these regression results to answer the following questions.

1. If a person if 43 years old and attended school for 16 years, what is his expected earnings?
2. Calculate a 95% confidence interval for your estimate in part a.
3. Are the coefficients statistically significant?  How do you know?
4. If our person in part a above went to school one less year and worked one more year, what would be his change in income?

Problem 3

The regression results on the next page use the discharge of CO₂ in metric tons from transportation in the US from 1949 to 2006 as the dependent variable.  The independent variable, t, is calculated at the year minus 1948, so t=1 for 1949, t = 2 for 1950, and so on until t = 58 for 2006.  Use the results on the next page to answer the following questions. 

1. Use the regression report below to write down the equation from these results.
2. Forecast CO₂ emissions in metric tons for 2010. 
3. Since this regression uses time-series data, what problems might arise and how can these be identified?
4. What does the R² statistic tell you?