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 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 $6000 per year. (Note: Dist to college was measured in 100’s of miles, tuition was measured in $1000s)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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
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)
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The output appears below. |
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Regression Statistics |
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Multiple R |
0.4275 |
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R Square |
0.1827 |
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Adjusted R Square |
0.1784 |
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Standard Error |
1.5259 |
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Observations |
943 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
5 |
487.8758 |
97.5752 |
41.9053 |
0.0000 |
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Residual |
937 |
2181.7743 |
2.3285 |
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Total |
942 |
2669.6501 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
9.4074 |
0.5182 |
18.1532 |
0.0000 |
8.3904 |
10.4244 |
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Unemployment rate |
0.0213 |
0.0252 |
0.8452 |
0.3982 |
-0.0281 |
0.0707 |
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County Hr Wage |
0.0334 |
0.0498 |
0.6698 |
0.5032 |
-0.0644 |
0.1311 |
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Test |
0.0831 |
0.0062 |
13.5039 |
0.0000 |
0.0710 |
0.0952 |
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Dist to 4 yr college |
-0.0390 |
0.0213 |
-1.8284 |
0.0678 |
-0.0809 |
0.0029 |
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tuition (in $1000) |
-0.6266 |
0.2637 |
-2.3761 |
0.0177 |
-1.1442 |
-0.1090 |
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 $6000 per year. (Note: Dist to college was measured in 100’s of miles, tuition was measured in $1000s)
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