StatCrunch logo (home)

Report Properties

from Flickr
Created: Mar 9, 2010
Share: yes
Views: 22858
Results in this report
Data sets in this report
Need help?
To copy selected text, right click to Copy or choose the Copy option under your browser's Edit menu. Text copied in this manner can be pasted directly into most documents with formatting maintained.
To copy selected graphs, right click on the graph to Copy. When pasting into a document, make sure to paste the graph content rather than a link to the graph. For example, to paste in MS Word choose Edit > Paste Special, and select the Device Independent Bitmap option.
You can now also Mail results and reports. The email may contain a simple link to the StatCrunch site or the complete output with data and graphics attached. In addition to being a great way to deliver output to someone else, this is also a great way to save your own hard copy. To try it out, simply click on the Mail link.
The Relation Between Educational Level and Income
Mail   Print   Twitter   Facebook

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.


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.


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.


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.


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]
Right click to copy

Result 2: Correlation   [Info]
Correlation between % with Bachelor's and Personal Income is:

Result 3: Simple Linear Regression income/education   [Info]
Right click to copy

Result 4: Boxplot income/education   [Info]
Right click to copy

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.

Data set 1. Income versus Education   [Info]
To analyze this data, please sign in.

HTML link:
<A href="">The Relation Between Educational Level and Income</A>

Want to comment? Subscribe
Already a member? Sign in.
By msullivan13803
Mar 22, 2010

Would like to see an interpretation of slope. If the percent of the population with a Bachelor's increases by 1, the per capita income increases by $735, on average.
By jcolon1323
Mar 10, 2010

Your report is very neat and detailed. It's easy to understand, nice job. Jackie Colon

Always Learning