Outliers · Exercise 14

The percent of women who are wage and salary workers who are paid hourly rates is given in for a 14-year period.

$$\begin{array}{cc}\text{Year}& \text{Percent of workers paid hourly rates}\\ \text{1}& \text{61.2}\\ \text{2}& \text{60.7}\\ \text{3}& \text{61.3}\\ \text{4}& \text{61.3}\\ \text{5}& \text{61.8}\\ \text{6}& \text{61.7}\\ \text{7}& \text{61.8}\\ \text{8}& \text{62.0}\\ \text{9}& \text{62.7}\\ \text{12}& \text{62.8}\\ \text{14}& \text{62.9}\end{array}$$

(a) Using “year” as the independent variable and “percent” as the dependent variable, draw a scatter plot of the data.
(b) Does it appear from inspection that there is a relationship between the variables? Why or why not?
(c) Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
(d) Find the correlation coefficient. Is it significant?
(e) Find the estimated percents for year 13 and year 10.
(f) Based on the data, is there a linear relationship between the year and the percent of female wage and salary earners who are paid hourly rates?
(g) Are there any outliers in the data?
(h) What is the estimated percent for the year 72? Does the least-squares line give an accurate estimate for that year? Explain why or why not.
(i) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Introductory Statistics 2e · §12.6 Outliers · Exercise 14