MATH 1281-01 - AY2024-T2
Explain the difference between R2 and adjusted R2. Which one will be higher? Which one, according to you, is a better measure of the strength of a linear regression model?
R² shows the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It ranges from 0 to 1, where 0 indicates that the model doesn’t fit the data, and 1 indicates that the model explains all the variability of the response data around its mean.
On the other hand, adjusted R
2
represents the percentage of variation explained by only the independent variables that actually affect the dependent variable.
Adjusted R
2
is normally lower than R
2
, and it is a better measure of the strength of a linear regression model when there are many independent variables.
2. Justify your answer with relevant examples.
Let us consider an example of selling a used car. We predict the price of the car depending on the
fuel consumption, engine power, comfort of the seats and the number of passenger seats. In such a case, the adjusted R
2
is a better option since we have multiple independent variables.
Reference
.
Diez, D. M., Barr, C. D., & Çetinkaya-Rundel, M. (2019). Openintro statistics - Fourth edition. Open Textbook Library.
https://www.biostat.jhsph.edu/~iruczins/teaching/books/2019.openintro.statistics.pdf
