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<!DOCTYPE html>
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    <title>Regression - Statistics Study Guide</title>
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    <header>
        <h1>Regression - Statistics Study Guide</h1>
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        <a href="index.html">Back to Study Guide</a>
        <a href="statistics.html">Back to Statistics</a>
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        <h2>Understanding Regression</h2>

        <p>**Regression** is a statistical method used for estimating the relationships among variables. In simple linear regression, the goal is to predict the value of a dependent variable based on the value of an independent variable.</p>

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                <h4>What is Regression?</h4>
                <p>Regression analysis seeks to model the relationship between two or more variables by fitting a line (or curve) to the data points. This model can then be used for prediction or understanding the relationships.</p>
            </div>
        </div>

        <h3>Types of Regression</h3>
        <div class="example-box">
            <p><strong>Simple Linear Regression:</strong> Involves one independent variable and one dependent variable, and the relationship between them is modeled as a straight line.</p>
            <p><strong>Multiple Linear Regression:</strong> Extends simple linear regression by using multiple independent variables to predict the dependent variable.</p>
        </div>

        <h3>Example: Simple Linear Regression</h3>
        <div class="example-box">
            <p><strong>Example 1:</strong> Let's say we are trying to predict a person's weight based on their height. Using simple linear regression, we fit a line to the data points to estimate the weight (dependent variable) for a given height (independent variable).</p>
            <pre>Weight = m * Height + b</pre>
        </div>

        <h3>Example: Multiple Linear Regression</h3>
        <div class="example-box">
            <p><strong>Example 2:</strong> In multiple linear regression, we may want to predict a person's salary based on their years of experience and education level. The model would look something like this:</p>
            <pre>Salary = m1 * Experience + m2 * Education + b</pre>
        </div>

        <h3>Try It Yourself:</h3>
        <p>Consider the following data of study hours (X) and test scores (Y). Try fitting a line to this data using simple linear regression:</p>
        <pre>Study Hours: [1, 2, 3, 4, 5]</pre>
        <pre>Test Scores: [55, 60, 65, 70, 75]</pre>
        <p>What would be the predicted test score for 6 hours of study? Use the formula for simple linear regression to estimate the slope (m) and intercept (b), and calculate the predicted value.</p>

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