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.
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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, R^{2}, is 0.748, therefore 74.8% of the variation in the response variables is explained by the leastsquares regression line. The other 25.2% must be determined by other factors.
The yintercept 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 yintercept 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

Correlation between % with Bachelor's and Personal Income is:
0.8647107 


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 Rsq = 0.74772453 Estimate of error standard deviation: 1581.6168 Parameter estimates:
Analysis of variance table for regression model:
Predicted values:
Residuals stored in new column, Residuals. 