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California State University, Monterey Bay *

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1281

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Mathematics

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Nov 24, 2024

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MATH 1281-01 - AY2024-T2 Let's consider a scenario where a company aims to predict employee productivity based on factors like hours worked, experience, and education level, in this regression analysis, R-squared (R2) and adjusted R-squared play crucial roles in evaluating the model's effectiveness, because R-squared measures the proportion of variation in employee productivity that's explained by the included factors. If the model only considers hours worked, the R2 might be, let’s say, 0.60, indicating that 60% of the variation in productivity can be explained by hours worked alone, adding experience and education level might increase R2 to 0.75, showing an improvement in explaining productivity variance, however, adding too many irrelevant factors, such as the number of pets employees own or their favorite food, might artificially inflate R2, this is where adjusted R-squared becomes valuable, adjusted R-squared considers model simplicity by penalizing the addition of unnecessary variables, let's say the initial model with hours worked, experience, and education level yields an R2 of 0.75 but an adjusted R2 of 0.74. However, if additional frivolous variables are added, the adjusted R2 might drop to 0.70, indicating that these extra variables are not enhancing the model significantly. Diez, D., Cetinkaya-Rundel, M., Barr C. D., & Barr, C. D. (2019) In essence, R2 tends to increase with each added variable, whether relevant or not, which might overestimate the model's accuracy. In contrast, adjusted R2 adjusts for the number of predictors, offering a more realistic assessment of the model's performance, which helps in distinguishing between a model that's genuinely better versus one that seems improved just because more factors are included, more also, in our example, while R2 might suggest a higher percentage of explained variance with more variables, adjusted R2 helps identify the trade-off between model complexity and explanatory power, it guides us to prioritize relevant predictors and avoid the inclusion of extraneous variables that don't substantially contribute to explaining employee productivity. Conclusively, adjusted R-squared is generally a more reliable metric, especially when comparing models with different numbers of predictors, as it accounts for model complexity and guards against overfitting by emphasizing the significance of genuinely influential variables. Reference Diez, D., Cetinkaya-Rundel, M., Barr C. D., & Barr, C. D. (2019). OpenIntro statistics - Fourth

edition. Open Textbook Library. https://www.biostat.jhsph.edu/~iruczins/teaching/books/2019.openintro.statistics.pdf

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