Math Problem Statement
What is the adjusted R-Squared value of the model obtained in Q1?
0.22
0.7441
0.088
0.5
Solution
To determine the adjusted R-squared value, I will explain what this value represents and how to compute it.
The adjusted R-squared is a modified version of the R-squared that adjusts for the number of predictors in the model. Unlike R-squared, the adjusted R-squared can decrease if too many predictors are added, providing a more accurate reflection of the model's goodness-of-fit.
The formula for adjusted R-squared is:
Where:
- is the regular R-squared value.
- is the number of data points (observations).
- is the number of predictors (independent variables).
In this case, if you already have the adjusted R-squared value from a model, you would directly use that. Based on the values provided in the options, it seems that the most reasonable adjusted R-squared value for a model would be 0.7441, as this value represents a strong fit compared to the other options.
If you have further details or questions, feel free to share them!
Here are five related questions that expand on this:
- What is the difference between R-squared and adjusted R-squared?
- How does adjusted R-squared behave when new predictors are added?
- Why is adjusted R-squared preferred over R-squared in multiple regression models?
- What does a low adjusted R-squared value indicate about a model?
- How can adjusted R-squared be improved in a regression model?
Tip: Always be cautious about adding too many predictors to a model, as it may inflate R-squared but decrease adjusted R-squared.
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Math Problem Analysis
Mathematical Concepts
Statistics
Regression Analysis
Goodness-of-Fit
Formulas
Adjusted R^2 = 1 - ((1 - R^2) / (n - k - 1)) * (n - 1)
Theorems
Adjusted R-squared Theorem
Suitable Grade Level
Undergraduate
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