Problem

Given the following pairs of data points: (2, 3), (3, 4), (4, 5), (5, 6), and (6, 7). Find the linear correlation coefficient.

Answer

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Answer

Simplify the expression to get the final answer: r=375−500(270−400)(395−625)

Steps

Step 1 ：First, we compute the sums of the x values, the y values, the square of the x values, the square of the y values, and the product of the x and y values.∑x=2+3+4+5+6=20,∑y=3+4+5+6+7=25,∑x2=22+32+42+52+62=54,∑y2=32+42+52+62+72=79,∑xy=2∗3+3∗4+4∗5+5∗6+6∗7=75

Step 2 ：Next, we substitute these sums into the formula for the linear correlation coefficient r: r=n∑xy−∑x∑y(n∑x2−(∑x)2)(n∑y2−(∑y)2)

Step 3 ：Substitute the values into the formula: r=5∗75−20∗25(5∗54−202)(5∗79−252)

Step 4 ：Simplify the expression to get the final answer: r=375−500(270−400)(395−625)

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