Given: y = –5 + 7x

To find: value of r

Solution:

We can rewrite the given equation in the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

y = 7x - 5

Comparing with the slope-intercept form, we get:

m = 7 and b = -5

The correlation coefficient r measures the strength and direction of the linear relationship between two variables. It takes values between -1 and 1, where a value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

The formula to calculate r is:

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

where n is the number of observations, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, Σx^2 is the sum of the squares of x, and Σy^2 is the sum of the squares of y.

Since we have only one variable (x) and its corresponding values of y, we cannot calculate the correlation coefficient r.

Therefore, the answer is (d) none.

Alternate Method:

We can also determine the value of r using the formula:

r = √(m^2) / (m^2 + 1)

where m is the slope of the line.

Substituting the value of m, we get:

r = √(7^2) / (7^2 + 1)

r = √49 / 50

r = 0.98

Since the value of r is not one of the options given, the answer is still (d) none.