Challenge: Fitting The Linear Regression Model

Darwin’s wild Mignonette data

The Mignonette data (Darwin 1877)Darwin, Charles. The Effects of Cross and Self Fertilisation in the Vegetable Kingdom. Appleton and Company, New York 1877. compares the heights of cross-pollinated plants with self-pollinated plants. Plants were paired within the pots they were grown in.

Format

This data frame contains the following columns:

• cross: heights of the cross-pollinated plants.
• self: heights of the self-pollinated plants.

Problem statement

Write a piece of code in R that reads Mignonette’s data frame from the DAAG package, and do the following operations:

• Display the first few rows of Mignonette’s data frame.

• Produce a table of the summary statistics.

• Fit the linear regression model to the Mignonette data.

Output

# cross   self
# 1 21.000 12.875
# 2 14.250 16.000
# 3 19.125 11.875
# 4  7.000 15.250
# 5 15.125 19.125
# 6 20.500 12.500
#     cross            self       
# Min.   : 7.00   Min.   : 7.875  
# 1st Qu.:14.91   1st Qu.:12.781  
# Median :17.56   Median :14.625  
# Mean   :17.18   Mean   :14.620  
# 3rd Qu.:20.56   3rd Qu.:16.250  
# Max.   :25.25   Max.   :20.875  
# lm(formula = cross ~ self, data = mignonette)
#            coef.est coef.se
# (Intercept) 19.38     4.78  
# self        -0.15     0.32  
---
# n = 24, k = 2
# residual sd = 4.80, R-Squared = 0.01

Coding exercise

This problem has been designed for you to practice freely, so try to solve it on your own first. Take some time and think about the different concepts that we’ve explored in this course so far.

If you’re feeling stuck, you can always check out the solution in the next lesson.

Good luck!