Question

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
	df	SS	MS	F	Significance F
Regression	5	487.8758	97.5752	41.9053	0.0000
Residual	937	2181.7743	2.3285
Total	942	2669.6501
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 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 yr 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?
   1. Unemployment rate, test scores and distance to college
   2. Unemployment rate, Manufacturing wage, test scores, distance to 4 yr college, and tuition
   3. Test scores, Distance to 4 year college, and tuition
   4. Test scores

2. How much of the variation in the dependent variable is explained by variation in the explanatory variables?
   1. 18.27% of variation in the unemployment rate is explained by County Hr Wage, Test, Dist to 4 yr college, and tuition
   2. 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
   3. 42.75% of variation in the unemployment rate is explained by County Hr Wage, Test, Dist to 4 yr college, and tuition
   4. 42.75% of variation in years of education completed is explained by Unemployment rate, County Hr Wage, Test, Dist to 4 yr college, and tuition

Answer 1

Ans 1 )Using the at the .10 significance level, the variables appear to be linearly related to the years of education completed is give by option c because their p-value is less than 0.10

c)Test scores, Distance to 4-year college, and tuition

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

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