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The Relation Between Educational Level and Income
Generated Mar 9, 2010 by lalalalauren86

This report illustrates the relationship between educational level and income, specifically the percentage of people who have bachelor's degrees and the average personal income.

<result#1>

This scatter diagram shows a few things about the relationship between the variables. The percent of people with Bachelor's degrees is treated as the explanatory variable, while the personal income is treated as the response variable. By looking at the graph, it is evident that the two variables have a positive association, that is, when one value increases, the other also increases. The points also seem to resemble a line, showing a possible linear relation.

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The correlation between the variables is listed as 0.8647107. According to Table 2 in Appendix A of Statistics: Informed Decisions Using Data, 3E, for a data set of 12, the critical value for the correlation coefficient is 0.576. Because the correlation coefficient for this set of data is greater than the critical value, the variables have a linear relation.

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This table indicates that the coefficient of determination, R2, is 0.748, therefore 74.8% of the variation in the response variables is explained by the least-squares regression line. The other 25.2% must be determined by other factors.

The y-intercept is 14,772.605, so when the value of x is equal to 0, meaning there are zero people with Bachelor's degrees, the average personal income is predicted to be about $14,772.61.

The slope of the line is 735.4252, so the linear equation is y=735.4252x + 14772.605. the positive values of the slope and y-intercept further confirm that the relationship between the variables is positive.

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This boxplot shows no outliers, so there are no values that significantly affect the linear equation.

In conclusion, this data set illustrates that, as the percentage of people with Bachelor's degree increases, the average personal income also increases.

 

 

 

-Lauren Bibeau

Result 1: Scatter Plot income/education   [Info]
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Result 2: Correlation   [Info]
Correlation between % with Bachelor's and Personal Income is:
0.8647107



Result 3: Simple Linear Regression income/education   [Info]
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Result 4: Boxplot income/education   [Info]
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Result 5: Simple Linear Regression 2   [Info]
Simple linear regression results:
Dependent Variable: Personal Income
Independent Variable: % with Bachelor's
Personal Income = 14772.605 + 735.4252 % with Bachelor's
Sample size: 9
R (correlation coefficient) = 0.8647
R-sq = 0.74772453
Estimate of error standard deviation: 1581.6168

Parameter estimates:
Parameter Estimate Std. Err. DF T-Stat P-Value
Intercept 14772.605 4086.7126 7 3.6147895 0.0086
Slope 735.4252 161.45674 7 4.5549364 0.0026


Analysis of variance table for regression model:
Source DF SS MS F-stat P-value
Model 1 5.1899984E7 5.1899984E7 20.747446 0.0026
Error 7 1.7510584E7 2501512
Total 8 6.9410568E7


Predicted values:
X value Pred. Y s.e.(Pred. y) 95% C.I. 95% P.I.
1 15508.031 3926.6604 (6222.9546, 24793.107) (5498.0503, 25518.012)


Residuals stored in new column, Residuals.