Module 12: Linear Regression and Correlation
Section Exercises
Barbara Illowsky & OpenStax et al.
Linear Equations
Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour.
4. Find the equation that expresses the total fee in terms of the number of days the payment is late.
6. Is the equation y = 10 + 5x – 3x2 linear? Why or why not?
a. y = 6x + 8
b. y + 7 = 3x
c. y – x = 8x2
d. 4y = 8
8. Does the graph show a linear equation? Why or why not?
The table below contains real data for the first two decades of AIDS reporting.
| Year | # AIDS cases diagnosed | # AIDS deaths |
| Pre-1981 | 91 | 29 |
| 1981 | 319 | 121 |
| 1982 | 1,170 | 453 |
| 1983 | 3,076 | 1,482 |
| 1984 | 6,240 | 3,466 |
| 1985 | 11,776 | 6,878 |
| 1986 | 19,032 | 11,987 |
| 1987 | 28,564 | 16,162 |
| 1988 | 35,447 | 20,868 |
| 1989 | 42,674 | 27,591 |
| 1990 | 48,634 | 31,335 |
| 1991 | 59,660 | 36,560 |
| 1992 | 78,530 | 41,055 |
| 1993 | 78,834 | 44,730 |
| 1994 | 71,874 | 49,095 |
| 1995 | 68,505 | 49,456 |
| 1996 | 59,347 | 38,510 |
| 1997 | 47,149 | 20,736 |
| 1998 | 38,393 | 19,005 |
| 1999 | 25,174 | 18,454 |
| 2000 | 25,522 | 17,347 |
| 2001 | 25,643 | 17,402 |
| 2002 | 26,464 | 16,371 |
| Total | 802,118 | 489,093 |
Use the following information to answer the next two exercises. A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y = 50 + 100x.
10. What are the independent and dependent variables?
Use the following information to answer the next three questions. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x.
12. What are the independent and dependent variables?
13. How many pounds of soil does the shoreline lose in a year?
14. What is the y-intercept? Interpret its meaning.
Use the following information to answer the next two exercises. The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is y = 15 – 1.5x where x is the number of hours passed in an eight-hour day of trading.
- A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers.
- A study is done to determine if the weekly grocery bill changes based on the number of family members.
- Insurance companies base life insurance premiums partially on the age of the applicant.
- Utility bills vary according to power consumption.
- A study is done to determine if a higher education reduces the crime rate in a population.
18. Piece-rate systems are widely debated incentive payment plans. In a recent study of