A small company has five employees. The following table presents the number of years each has been employed (x) and the hourly wage in dollars (y).

a. Compute ̄x, ̄y, sx, and sy.

b. Compute the correlation coefficient between years of service and hourly wage.

c. Each employee is given a raise of $1.00 per hour, so each y-value is increased by 1.

Using these new y-values, compute the sample mean ̄y and the sample standard deviation sy.

d. In part (c), each y-value was increased by 1.

What was the effect on ̄y? What was the effect on sy?

e. Compute the correlation coefficient between years of service and the increased hourly wage. Explain why the correlation coefficient is unchanged even though the y-values have changed.

f. Convert x to months by multiplying each x-value by 12.

So the new x-values are 6, 12, 21, 30, and 36.

Compute the sample mean ̄x and the sample standard deviation sx.

g. In part (f), each x-value was multiplied by 12.

What was the effect on ̄x and sx?

h. Compute the correlation coefficient between months of service and hourly wage in dollars. Explain why the correlation coefficient is unchanged even though the x-values, ̄x, and sx have changed.

i. Use the results of parts (a)–(h) to fill in the blank: If a constant is added to each x-value or to each y-value, the correlation coefficient is _________________ .

j. Use the results of parts (a)–(h) to fill in the blank:
If each x-value or each y-value is multiplied by a positive constant, the correlation coefficient is ______________________ .

Transcribed Image Text:

x (years) 0.5 1.0 1.75 2.5 3.0 y (dollars) 9.51 8.23 10.95 12.70 12.75