Questions: Use technology to find an equation of the line of best fit for the data. Round your answers to the hundredths place. Equation: y=-.8x+5 Identify the correlation coefficient.

Solution Steps

The provided equation of the line of best fit is \(y = -0.8x + 5\). We can use this equation to identify two points on the line.

Let \(x = 0\), then \(y = -0.8(0) + 5 = 5\). So, one point is \((0, 5)\). Let \(x = 5\), then \(y = -0.8(5) + 5 = 1\). So, another point is \((5, 1)\).

Using the two points \((0, 5)\) and \((5, 1)\), we can calculate the difference in x-values and y-values. Difference in x: \(5 - 0 = 5\) Difference in y: \(1 - 5 = -4\)

The line of best fit has a negative slope, indicating a negative correlation. The points are relatively close to the line, suggesting a strong correlation. Since the correlation coefficient ranges from -1 to 1, where -1 represents a perfect negative correlation and 1 represents a perfect positive correlation, we can estimate the correlation coefficient to be close to -1.

The given equation \(y = -0.8x + 5\) suggests a strong negative correlation. By observing the graph, the points cluster fairly close to the line of best fit, but not perfectly. Therefore, the correlation coefficient should be a negative value close to -1. A reasonable estimate, based on the scatter plot and the equation, would be around -0.9.

Final Answer