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SOCCER The table shows the number of goals a soccer team scored each season since 2010. Let x be the number of years since 2010. Year201020112012201320142015 Goals Scored485250464842 a. Write the equation for the best-fit line for the data. Round to the nearest hundredth, if necessary. b. Find and interpret the correlation coefficient.

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Final answer:

To write the equation for the best-fit line for the data, find the slope and y-intercept, and use the formula. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

Step-by-step explanation:

a. To write the equation for the best-fit line for the data, we need to find the slope and y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (nΣxy - (Σx)(Σy)) / (nΣx^2 - (Σx)^2)

To find the y-intercept, we can use the formula:

b = (Σy - mΣx) / n

After calculating the values, we can substitute them into the equation and round to the nearest hundredth, if necessary.

b. The correlation coefficient measures the strength and direction of the linear relationship between two variables. To find the correlation coefficient, we can use the formula:

r = (nΣxy - (Σx)(Σy)) / (√(nΣx^2 - (Σx)^2)√(nΣy^2 - (Σy)^2))

We can then interpret the correlation coefficient based on its value.

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