Simple Linear Regression Assessment For Breast Cancer Synthetic Data

Isabelle Rennenberg



West Chester University

Table of Contents

  • Breast Cancer Data
  • All Contents of Data
  • Cancer Cell Mitoses
  • Numerical Variable Analysis
  • Plot of Mitoses and Cell Thickness
  • Regression Output
  • Regression Equation
  • Conclusions
  • Output Reference

Breast Cancer Data

  • The data used for this presentation was synthetic data
  • This data included 11 variables (10 numeric, 1 categorical)
  • There was a total of 600 observations
  • The variables used for this analysis were:
    • Mitoses (cell growth) as the independent variable
    • Thickness of clump (thickness of the layers of the cells) as the dependent variable
  • This assessment had the aim of understanding if there is a relationship between mitoses (number of cell divisions) and thickness of cell clumps

All Contents of Data

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Cancer Cell Mitoses

Numerical Variable Analysis

Variable Mean
Mitoses 2.09
Cell Thickness 5.41

Plot of Mitoses and Cell Thickness



  • As the number of cell divisions increases, there are less cells that have a small amount of layers.

Regression Output



  • The p value for mitoses was highly significant at <0.0001.
    • This indicates that cell division is related to cell thickness. The greater the cell division, the thicker the cells.

Regression Equation

  • \(y=4.27157+X_{mitoses}0.54383\)
    • For each increase of cell mitoses, cell thickness is multiplied by 0.54

Conclusions

  • For the synthetic breast cancer data, a simple linear regression was performed.
  • The independent variable, mitoses, was evaluated to see if increase/decrease of cell division impacted cell thickness (dependent variable)
  • It was found that there was a strong relationship between mitoses and thickness, with a p value of <0.0001
    • Furthermore, it was found that with increased cell division, cells were thicker
    • Increased cell division and increased layers of cells are both related to a higher tendency for cells to not be benign
  • The final regression equation was: \(y=4.27157+X_{mitoses}0.54383\)

Output Reference

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