Subjects statistics

Line Best Fit 8249F9

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1. The problem is to find the line of best fit for a given scatter plot. 2. The line of best fit is a linear equation of the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. To find $m$ and $b$, we use the formulas: $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y - m \sum x}{n}$$ where $n$ is the number of points, $\sum xy$ is the sum of the products of $x$ and $y$ values, $\sum x$ and $\sum y$ are sums of $x$ and $y$ values respectively, and $\sum x^2$ is the sum of squares of $x$ values. 4. Using the graphing tool, input the scatter plot data points. 5. The tool calculates the slope $m$ and intercept $b$ automatically. 6. The resulting line of best fit equation is displayed as $$y = mx + b$$. 7. This line minimizes the sum of squared vertical distances from each data point to the line, providing the best linear approximation.