Question

A manager wishes to find out whether there is a relationship between the age of his

employees and the number of sick days they take each year. The data for the sample

follow.

Age, x 18 26 39 48 53 58

Days, y 16 12 9 5 6 2

a. Make a scatter plot

b. Compute the correlation coefficient

c. Find the equation of the regression line

Answer 1

a)

b)

correlation coefficient:

$r=\frac{Σ(x_i - x̄)(y_i - ȳ)}{\sqrt{Σ(x_i - x̄)^2Σ(y_i - ȳ)^2 }}=-0.9791$

c)

regression line:

$y=b_0+b_1x$

$b_1 =\frac{\sum(x_i-x̄)(y_i-ȳ)}{Σ(x_i-x̄)^2}=-0.3165$

$b_0 = ȳ - b_1x̄=21.1005$

$y=21.1005-0.3165x$