A rural state wants to encourage high school graduates to continue their education and attend college. The state collected information on a random sample of high school seniors from across the state 7 years ago and is now observing how many years of education they completed. They believe students decide to achieve more education when they are more capable, have easier access to college education, and the opportunity cost of attending are lower. To explore the factors that affect the years of education completed they have used multiple regression to estimate the years of completed education as a function of:

Unemployment rate - the unemployment rate in the county (3.9-16.8)
County Hr Wage - average starting hourly manufacturing wage in the county
Test - student score on college admission test (0 to 100 scale)
Dist to college - Distance to near college (measured in 100's of miles)
Tuition - Tuition charged at nearest state university (measured in $1000s)

The output appears below.
Regression Statistics
Multiple R 0.4275
R Square 0.1827
Adjusted R Square 0.1784
Standard Error 1.5259
Observations 943

ANOVA
Significance
df SS MS F F
Regression 5 487.8758 97.5752 41.9053 0.0000
Residual 937 2181.7743 2.328
Total 942 2669.6501

Standard Upper
Coefficients Error t Stat P-value Lower 95% 95%
Intercept 9.4074 0.5182 18.1532 0.0000 8.3904 10.4244
Unemployment rate 0.0213 0.0252 0.8452 0.3982 -0.0281 0.0707
County Hr Wage 0.0334 0.0498 0.6698 0.5032 -0.0644 0.1311
Test 0.0831 0.0062 13.5039 0.0000 0.0710 0.0952
Dist to 4 y college -0.0390 0.0213 -1.8284 0.0678 -0.0809 0.0029
tuition (in $1000 -0.6266 0.2637 -2.3761 0.0177 -1.1442 -0.1090

1. Using the at the 10 significance level, which of the following variables appear to be linearly related to the years of education completed?

a) Unemployment rate, test scores and distance to college.
b) Unemployment rate, Manufacturing wage, test scores, distance to 4 y college, and tuition.
c) Test scores, Distance to 4 year college, and tuition.
d) Test scores.

2. How much of the variation in the dependent variable is explained by variation in the explanatory variables?

a) 18.27% of variation in the unemployment rate is explained by County Hr Wage, Test, Dist to 4 yr college, and tuition.
b) 18.27% of variation in years of education completed is explained by Unemployment rate, County Hr Wage, Test, Dist to 4 yr college, and tuition.
c) 42.75% of variation in the unemployment rate is explained by County Hr Wage, Test, Dist to 4 y college, and tuition.
d) 42.75% of variation in years of education completed is explained by Unemployment rate, County Hr Wage, Test, Dist to 4 y college, and tuition.

3. Senator Key believes the further a student has to travel from their high school to attend college, the less education they will obtain. He thinks the problem is that many students live too far away from a 4-year university and education levels would be higher if the state built more college campuses in areas that currently do not have a nearby campus. Does this analysis provide evidence to support Senator Kcy's hypothesis at the .10 significance level?

a) Yes
b) No
c) Not enough information to determine
d) The proper analyses were not performed

4. How would you interpret the coefficient on Test?

a) Students with test scores in the top 8% were most likely to attend college
b) Doing well on the test improves the likelihood of graduating from college by .08.
c)Students who attended college improved their test scores by .0831.
d) For each one point increase in test scores the predicted years of education increases by .083 years.

5. At the .05 significance level, is there evidence that students are responding to the high unemployment rate in their county when choosing how much education to obtain?

a) Yes
b) No
c) Not enough information to determine
d) The proper analyses were not performed

6. What is the predicted years of education completed for a student graduating from high school in a county with a starting manufacturing wage of $11.20 per hour, an unemployment rate of 3.9%, who has a test score of 80 and the nearest university is 125 miles away and charges tuition of 50000 per year? (Note: Rist to college was measured in 100's of miles, tuition was measured in $1000s).

a) 7.79 b) 12.70 c) 13.52 d) 15.83