Question

You are given the following information about x and y:

X - Independent variable: 1, 2, 3, 4, 5
Y - Dependent variable: 5, 4, 3, 2, 1
Refer to Exhibit 14-5. The sample correlation coefficient equals:
Options:
a) -1
b) 0
c) 1
d) Cannot be determined from the information provided

Answer 1

The correlation coefficient cannot be determined from the given information.

Step-by-step explanation:

First, let's calculate the correlation coefficient using the given data. The formula for calculating the correlation coefficient is:

r = [(n * ∑(x * y)) - (∑x * ∑y)] / sqrt([(n * ∑(x^2)) - (∑x^2)][(n * ∑(y^2)) - (∑y^2)])

Plugging the values from the given data into the formula, we get:

r = [(5 * (1 * 5 + 2 * 4 + 3 * 3 + 4 * 2 + 5 * 1)) - ((1 + 2 + 3 + 4 + 5) * (5 + 4 + 3 + 2 + 1))] / sqrt([(5 * (1^2 + 2^2 + 3^2 + 4^2 + 5^2)) - (1 + 2 + 3 + 4 + 5)^2][(5 * (5^2 + 4^2 + 3^2 + 2^2 + 1^2)) - (5 + 4 + 3 + 2 + 1)^2])

r = [-45] / sqrt([55 - 225][55 - 9])

r = -45 / sqrt([-170][-171])

As the denominator is negative, we divide the numerator and denominator by -1:

r = 45 / sqrt([170][171])

Since 170 and 171 are not perfect squares and their product is not a perfect square, we cannot simplify the square root. Therefore, we cannot determine the exact value of the correlation coefficient from the information provided.