12.12 Homework  (Page 2/7)

Use the AIDS data from the practice for this section , but this time use the columns “year #” and “# new AIDS deaths in U.S.” Answer all of the questions from the practice again, using the new columns.

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). (Source: Microsoft Bookshelf )

• a Using “stories” as the independent variable and “height” as the dependent variable, make a scatter plot of the data.
• b Does it appear from inspection that there is a relationship between the variables?
• c Calculate the least squares line. Put the equation in the form of: $\widehat{y}=a+\text{bx}$
• d Find the correlation coefficient. Is it significant?
• e Find the estimated heights for 32 stories and for 94 stories.
• f Use the two points in (e) to plot the least squares line on your graph from (b).
• g Based on the above data, is there a linear relationship between the number of stories in tall buildings and the height of the buildings?
• h Are there any outliers in the above data? If so, which point(s)?
• i What is the estimated height of a building with 6 stories? Does the least squares line give an accurate estimate of height? Explain why or why not.
• j Based on the least squares line, adding an extra story is predicted to add about how many feet to a building?
• k What is the slope of the least squares (best-fit) line? Interpret the slope.

Below is the life expectancy for an individual born in the United States in certain years. (Source: National Center for Health Statistics )

• a Decide which variable should be the independent variable and which should be the dependent variable.
• b Draw a scatter plot of the ordered pairs.
• c Calculate the least squares line. Put the equation in the form of: $\widehat{y}=a+\text{bx}$
• d Find the correlation coefficient. Is it significant?
• e Find the estimated life expectancy for an individual born in 1950 and for one born in 1982.
• f Why aren’t the answers to part (e) the values on the above chart that correspond to those years?
• g Use the two points in (e) to plot the least squares line on your graph from (b).
• h Based on the above data, is there a linear relationship between the year of birth and life expectancy?
• i Are there any outliers in the above data?
• j Using the least squares line, find the estimated life expectancy for an individual born in 1850. Does the least squares line give an accurate estimate for that year? Explain why or why not.
• k What is the slope of the least squares (best-fit) line? Interpret the slope.

The percent of female wage and salary workers who are paid hourly rates is given below for the years 1979 - 1992. (Source: Bureau of Labor Statistics, U.S. Dept. of Labor )

• a Using “year” as the independent variable and “percent” as the dependent variable, make 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: $\widehat{y}=a+\text{bx}$
• d Find the correlation coefficient. Is it significant?
• e Find the estimated percents for 1991 and 1988.
• f Use the two points in (e) to plot the least squares line on your graph from (b).
• g Based on the above data, is there a linear relationship between the year and the percent of female wage and salary earners who are paid hourly rates?
• h Are there any outliers in the above data?
• i What is the estimated percent for the year 2050? Does the least squares line give an accurate estimate for that year? Explain why or why not?
• j What is the slope of the least squares (best-fit) line? Interpret the slope.