Chapter 10: Linear Regression and Correlation
Chapter 10 Practice
Bring It Together from 10.6
The average number of people in a family that received welfare for various years is given in [link].
| Year | Welfare family size |
|---|---|
| 1969 | 4.0 |
| 1973 | 3.6 |
| 1975 | 3.2 |
| 1979 | 3.0 |
| 1983 | 3.0 |
| 1988 | 3.0 |
| 1991 | 2.9 |
- Using “year” as the independent variable and “welfare family size” as the dependent variable, draw a scatter plot of the data.
- Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
- Find the correlation coefficient. Is it significant?
- Pick two years between 1969 and 1991 and find the estimated welfare family sizes.
- Based on the data in [link], is there a linear relationship between the year and the average number of people in a welfare family?
- 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.
- Are there any outliers in the data?
- 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.
- 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 in [link] for the years 1979 to 1992.
| Year | Percent of workers paid hourly rates |
|---|---|
| 1979 | 61.2 |
| 1980 | 60.7 |
| 1981 | 61.3 |
| 1982 | 61.3 |
| 1983 | 61.8 |
| 1984 | 61.7 |
| 1985 | 61.8 |
| 1986 | 62.0 |
| 1987 | 62.7 |
| 1990 | 62.8 |
| 1992 | 62.9 |
- Using “year” as the independent variable and “percent” as the dependent variable, draw a scatter plot of the data.
- Does it appear from inspection that there is a relationship between the variables? Why or why not?
- Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
- Find the correlation coefficient. Is it significant?
- Find the estimated percentages for 1991 and 1988.
- 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?
- Are there any outliers in the data?
- 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.
- What is the slope of the least-squares (best-fit) line? Interpret the slope.
Solution
- Check student’s solution.
- yes
- ŷ = −266.8863+0.1656x
- 0.9448; Yes
- 62.8233; 62.3265
- yes
- yes; (1987, 62.7)
- 72.5937; no
- slope = 0.1656.
As the year increases by one, the percent of workers paid hourly rates tends to increase by 0.1656.
Use the following information to answer the next two exercises. The cost of a leading liquid laundry detergent in different sizes is given in [link].
| Size (ounces) | Cost (💲) | Cost per ounce |
|---|---|---|
| 16 | 3.99 | |
| 32 | 4.99 | |
| 64 | 5.99 | |
| 200 | 10.99 |
- Using “size” as the indepen