## Conditional means and standard deviation

The average cost per bachelor’s degree for private is $523.23 and the variation around the mean is $1,431.54 while the average cost per bachelor’s degree for the public is $37.96 and the variation around the mean is $130.28. The result shows that the return on investment is higher for private than public by $485.27. The variation is also higher for private than public.

Associates | Baccalaureate | Doctoral | Masters | Special Focus | Tribal | ||

Mean | 816.22 | 160.57 | 34.29 | 57.84 | 1159.25 | 415.85 | |

Std. Deviation | 1740.78 | 205.68 | 133.37 | 88.87 | 2191.21 | 605.34 | |

## Correlation

**The scatter plot suggests a weak negative relationship between returns on education and tuition fees. The correlation coefficient is -0.078 (p<0.0001) which means a weak negative but significant relationship exists between returns on education and tuition fees. The coefficient of determination is 0.006 which means only 0.6% of the variation in returns to education is explained by tuition fees. **

From the analysis so far, we see that private universities provide the best return on investment, similarly, universities whose Carnegie classification is special focus provides the best return on investment. More expensive institutions also provide a better return on investment compared to less expensive ones.

## Crosstabulation

Carnegie * sector Crosstabulation |
|||||

sector | Total | ||||

Private | Public | ||||

Carnegie | Associates | Count | 338 | 979 | 1317 |

% within sector | 13.2% | 61.0% | 31.7% | ||

Baccalaureate | Count | 438 | 88 | 526 | |

% within sector | 17.1% | 5.5% | 12.6% | ||

Doctoral | Count | 134 | 192 | 326 | |

% within sector | 5.2% | 12.0% | 7.8% | ||

Masters | Count | 466 | 269 | 735 | |

% within sector | 18.2% | 16.8% | 17.7% | ||

Special Focus | Count | 1172 | 49 | 1221 | |

% within sector | 45.9% | 3.1% | 29.4% | ||

Tribal | Count | 8 | 27 | 35 | |

% within sector | 0.3% | 1.7% | 0.8% | ||

Total | Count | 2556 | 1604 | 4160 | |

% within sector | 100.0% | 100.0% | 100.0% |