Введение в регрессионный анализ

In this classroom lecture, we walk step-by-step through modeling real-world data in Desmos by analyzing the relationship between daily hours spent on social media (X) and generalized anxiety scores (Y, GAD-7). Learn how to input data tables, configure graph settings and domain/range limits, plot a scatter plot, generate a linear regression line of best fit, and interpret statistical outputs like the correlation coefficient ($r$) and the coefficient of determination (R^2). We also cover how to make predictions using both interpolation and extrapolation, identify potential outliers, use inequalities to highlight thresholds (such as clinically significant anxiety scores), and briefly compare linear models against quadratic regressions. Timestamps 0:00 – Introduction: Modeling Data & Upcoming Regression Topics 2:05 – Getting Data into Desmos & Setting Up Tables 5:44 – Entering Social Media & Anxiety Data Points 7:38 – Adjusting Graph Settings: Domain, Range, and Axis Labels 10:46 – Analyzing the Scatter Plot (Social Media vs. GAD-7 Anxiety) 11:46 – Adding a Linear Regression Line of Best Fit 12:32 – Understanding Slope, Intercepts & Confounding Variables 15:45 – Explaining Correlation Coefficient (r) and R^2 19:06 – How Outliers Affect the Regression Line and R^2 20:10 – Exporting and Sharing Graphs from Desmos 21:17 – Interpolation vs. Extrapolation: Making Predictions 25:49 – Applying the GAD-7 Anxiety Threshold (Y greater than 10) & Graph Shading 30:31 – Exploring Other Regressions: Quadratic Models (ax^2 + bx + c) 32:10 – Next Steps: Direct Variation, Exponential Growth & Homework Review #lineart rRegression #Desmos #Statistics #DataAnalysis #MathTutorial #Algebra #STEM #ScatterPlot #JROspace_dot_info