To determine the equation of the line of best fit for the given data, we can perform a linear regression analysis. The data points are:
\[ \begin{align*} (1, 5) \ (2, 9) \ (3, 10) \ (4, 10.5) \ (5, 11) \ \end{align*} \]
Using a spreadsheet calculator or a statistics tool, you would calculate the slope (m) and y-intercept (b) for a linear equation of the form \( y = mx + b \).
Here are the calculations:
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Calculate the means of x and y:
- Mean of x = (1 + 2 + 3 + 4 + 5) / 5 = 3
- Mean of y = (5 + 9 + 10 + 10.5 + 11) / 5 = 9.1
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Calculate the coefficients:
- Slope (m) is calculated as: \[ m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \]
- Intercept (b) is calculated as: \[ b = \text{mean of } y - m(\text{mean of } x) \]
After performing these calculations, you would find that:
- \(m \approx 1.35\)
- \(b \approx 5.05\)
Thus, the equation of the line of best fit is:
\[ y \approx 1.35x + 5.05 \]
So, the correct response is:
y = 1.35x + 5.05