R-Squared Calculator

 

Introduction

R-squared, denoted as R^2, is a statistical measure that represents the proportion of the variance in a dependent variable that can be explained by an independent variable in a regression model. It is a crucial metric for assessing the goodness of fit of a regression model. To make this calculation easier, we’ll guide you through creating an HTML R-squared calculator, complete with the Sum of Squares of the Residuals (SSR), Total Sum of Squares (SST), and the R-squared value (R^2).

How to Use the R-Squared Calculator

To use the R-squared calculator, follow these steps:

  1. Enter your observed and predicted values into the calculator.
  2. Click the “Calculate R^2” button.
  3. The calculator will then compute the R-squared value based on the provided data.

Formula

The formula for calculating R-squared (R^2) is:

R^2 = 1 – (SSR/SST)

Where:

  • R^2 is the R-squared value.
  • SSR represents the Sum of Squares of the Residuals.
  • SST represents the Total Sum of Squares.

Example

Let’s work through a simple example to calculate R-squared using the given formula.

Suppose you have the following data:

Observed Values: [10, 15, 20, 25, 30] Predicted Values: [12, 14, 18, 22, 28]

First, calculate SSR and SST:

  • SSR = Σ(yi – ŷi)^2 = (10-12)^2 + (15-14)^2 + (20-18)^2 + (25-22)^2 + (30-28)^2 = 10
  • SST = Σ(yi – ȳ)^2 = (10-21)^2 + (15-21)^2 + (20-21)^2 + (25-21)^2 + (30-21)^2 = 90

Now, plug these values into the R-squared formula:

R^2 = 1 – (SSR/SST) = 1 – (10/90) = 1 – 0.1111 = 0.8889

So, the R-squared value for this example is approximately 0.8889.

Frequently Asked Questions (FAQs)

1. What does R-squared (R^2) measure?

R-squared measures the proportion of the variance in a dependent variable that can be explained by an independent variable in a regression model. It quantifies the goodness of fit of the model.

2. What does SSR stand for in the R-squared formula?

SSR stands for Sum of Squares of the Residuals. It represents the sum of the squared differences between the observed and predicted values in a regression model.

3. Can I use this R-squared calculator for multiple regression?

Yes, you can use this calculator for multiple regression by entering the observed and predicted values for each data point.

4. How can I implement this R-squared calculator in my website?

You can implement this calculator by embedding the HTML code provided in your website’s code, along with the necessary JavaScript in a <script> tag.

Conclusion

Calculating R-squared (R^2) is essential in regression analysis to assess how well a model fits the data. By creating an HTML R-squared calculator with the formula R^2 = 1 – (SSR/SST), you can easily determine the goodness of fit of your regression models. Use the provided code to integrate this calculator into your website, making it accessible to users with a convenient clickable button.

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