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:

Adjusted R2=1(1R2nk1)×(n1)\text{Adjusted } R^2 = 1 - \left( \frac{1 - R^2}{n - k - 1} \right) \times (n - 1)

Where:

  • R2R^2 is the regular R-squared value.
  • nn is the number of data points (observations).
  • kk 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:

  1. What is the difference between R-squared and adjusted R-squared?
  2. How does adjusted R-squared behave when new predictors are added?
  3. Why is adjusted R-squared preferred over R-squared in multiple regression models?
  4. What does a low adjusted R-squared value indicate about a model?
  5. 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