3.10 Bivariate descriptive statistics: homework  (Page 7/12)

Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows (Source: http:// http://www.census.gov/compendia/statab/cats/transportation/motor_vehicle_accidents_and_fatalities.html ):

• a For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80.)
• b Using “ages” as the independent variable and “Number of driver deaths per 100,000” as the dependent variable, make a scatter plot of the data.
• c Calculate the least squares (best–fit) line. Put the equation in the form of: $\widehat{y}=a+\text{bx}$
• d Find the correlation coefficient. Is it significant?
• e Pick two ages and find the estimated fatality rates.
• 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 age of a driver and driver fatality rate?
• h What is the slope of the least squares (best-fit) line? Interpret the slope.

The average number of people in a family that received welfare for various years is given below. (Source: House Ways and Means Committee, Health and Human Services Department )

• a Using “year” as the independent variable and “welfare family size” as the dependent variable, make a scatter plot of the data.
• b Calculate the least squares line. Put the equation in the form of: $\widehat{y}=a+\text{bx}$
• c Find the correlation coefficient. Is it significant?
• d Pick two years between 1969 and 1991 and find the estimated welfare family sizes.
• e Use the two points in (d) to plot the least squares line on your graph from (b).
• f Based on the above data, is there a linear relationship between the year and the average number of people in a welfare family?
• g Using the least squares line, estimate the welfare family sizes for 1960 and 1995. Does the least squares line give an accurate estimate for those years? Explain why or why not.
• h What is the estimated average welfare family size for 1986? 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.

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.