What is the adjusted R-Squared value of the model obtained in Q1?

0.22

0.7441

0.088

0.5

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:

\[
\text{Adjusted } R^2 = 1 - \left( \frac{1 - R^2}{n - k - 1} \right) \times (n - 1)
\]

Where:
- \( R^2 \) is the regular R-squared value.
- \( n \) is the number of data points (observations).
- \( k \) 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.

What is the adjusted R-Squared value of the model obtained in Q1?

Understand the adjusted R-squared value in a regression model. This explanation covers the formula for adjusted R^2, its relationship with R-squared, and its importance in multiple regression models. The most likely value of adjusted R-squared for the given model is 0.7441, indicating a strong fit.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation