CHAPTER 12: LINEAR REGRESSION AND
CORRELATION
A vacation resort rents SCUBA equipment to certified divers. The resort charges an
Exercise 1. up-front fee of $25 and another fee of $12.50 an hour.
What are the dependent and independent variables?
Solution dependent variable: fee amount; independent variable: time
Exercise 2. 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.
Find the equation that expresses the total fee in terms of the number of hours the
equipment is rented.
Solution y = 25 + 12.50x
Exercise 3. 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.
Graph the equation from Exercise 12.2.
Solution
A credit card company charges $10 when a payment is late, and $5 a day each
Exercise 4. day the payment remains unpaid.
Solution y = 10 + 5x
, A credit card company charges $10 when a payment is late, and $5 a day each
Exercise 5. day the payment remains unpaid.
Graph the equation from Exercise 12.4.
Solution
Exercise 6. Is the equation y = 10 + 5x – 3x2 linear? Why or why not?
Solution No, the equation is not linear because there is an exponent greater than one, and
the graph is therefore not a straight line.
Which of the following equations are linear?
Exercise 7. a. y = 6x + 8
b. y + 7 = 3x
c. y – x = 8x2
d. 4y = 8
Solution y = 6x + 8, 4y = 8, and y + 7 = 3x are all linear equations.
Exercise 8. Does the graph show a linear equation? Why or why not?
,Solution No, the graph does not show a linear equation because the graph is not a straight
line.
Exercise 9. Table 12.26 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
87 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 columns "year" and "# AIDS cases diagnosed. Why is “year” the
independent variable and “# AIDS cases diagnosed.” the dependent variable
(instead of the reverse)?
The number of AIDS cases depends on the year. Therefore, year becomes the
Solution independent variable and the number of AIDS cases is the dependent variable.
A specialty cleaning company charges an equipment fee and an hourly labor fee.
Exercise 10. A linear equation that expresses the total amount of the fee the company charges
for each session is y = 50 + 100x.
What are the independent and dependent variables?
, The independent variable (x) is the number of hours the company cleans. The
Solution dependent variable (y) is the amount, in dollars, the company charges for each
session.
Exercise 11. 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.
What is the y-intercept and what is the slope? Interpret them using complete
sentences.
The y-intercept is 50 (a = 50). At the start of the cleaning, the company charges a
Solution one-time fee of $50 (this is when x = 0). The slope is 100 (b = 100). For each
session, the company charges $100 for each hour they clean.
Due to erosion, a river shoreline is losing several thousand pounds of soil each
Exercise 12. year. A linear equation that expresses the total amount of soil lost per year is y =
12,000x.
What are the independent and dependent variables?
The independent variable (x) is the number of years gone by. The dependent
Solution variable (y) is the amount of soil, in pounds, the shoreline loses each year.
Exercise 13. 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.
How many pounds of soil does the shoreline lose in a year?
Solution 12,000 pounds of soil
Exercise 14. 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.
What is the y-intercept? Interpret its meaning.
The y-intercept is zero. This means that there was no fixed amount of soil that
Solution was lost before erosion began, which makes sense because the river shoreline
wouldn’t lose any soil if there were no erosion occurring.
The price of a single issue of stock can fluctuate throughout the day. A linear
Exercise 15. equation that represents the price of stock for Shipment Express is y = 15 – 1.5x
CORRELATION
A vacation resort rents SCUBA equipment to certified divers. The resort charges an
Exercise 1. up-front fee of $25 and another fee of $12.50 an hour.
What are the dependent and independent variables?
Solution dependent variable: fee amount; independent variable: time
Exercise 2. 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.
Find the equation that expresses the total fee in terms of the number of hours the
equipment is rented.
Solution y = 25 + 12.50x
Exercise 3. 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.
Graph the equation from Exercise 12.2.
Solution
A credit card company charges $10 when a payment is late, and $5 a day each
Exercise 4. day the payment remains unpaid.
Solution y = 10 + 5x
, A credit card company charges $10 when a payment is late, and $5 a day each
Exercise 5. day the payment remains unpaid.
Graph the equation from Exercise 12.4.
Solution
Exercise 6. Is the equation y = 10 + 5x – 3x2 linear? Why or why not?
Solution No, the equation is not linear because there is an exponent greater than one, and
the graph is therefore not a straight line.
Which of the following equations are linear?
Exercise 7. a. y = 6x + 8
b. y + 7 = 3x
c. y – x = 8x2
d. 4y = 8
Solution y = 6x + 8, 4y = 8, and y + 7 = 3x are all linear equations.
Exercise 8. Does the graph show a linear equation? Why or why not?
,Solution No, the graph does not show a linear equation because the graph is not a straight
line.
Exercise 9. Table 12.26 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
87 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 columns "year" and "# AIDS cases diagnosed. Why is “year” the
independent variable and “# AIDS cases diagnosed.” the dependent variable
(instead of the reverse)?
The number of AIDS cases depends on the year. Therefore, year becomes the
Solution independent variable and the number of AIDS cases is the dependent variable.
A specialty cleaning company charges an equipment fee and an hourly labor fee.
Exercise 10. A linear equation that expresses the total amount of the fee the company charges
for each session is y = 50 + 100x.
What are the independent and dependent variables?
, The independent variable (x) is the number of hours the company cleans. The
Solution dependent variable (y) is the amount, in dollars, the company charges for each
session.
Exercise 11. 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.
What is the y-intercept and what is the slope? Interpret them using complete
sentences.
The y-intercept is 50 (a = 50). At the start of the cleaning, the company charges a
Solution one-time fee of $50 (this is when x = 0). The slope is 100 (b = 100). For each
session, the company charges $100 for each hour they clean.
Due to erosion, a river shoreline is losing several thousand pounds of soil each
Exercise 12. year. A linear equation that expresses the total amount of soil lost per year is y =
12,000x.
What are the independent and dependent variables?
The independent variable (x) is the number of years gone by. The dependent
Solution variable (y) is the amount of soil, in pounds, the shoreline loses each year.
Exercise 13. 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.
How many pounds of soil does the shoreline lose in a year?
Solution 12,000 pounds of soil
Exercise 14. 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.
What is the y-intercept? Interpret its meaning.
The y-intercept is zero. This means that there was no fixed amount of soil that
Solution was lost before erosion began, which makes sense because the river shoreline
wouldn’t lose any soil if there were no erosion occurring.
The price of a single issue of stock can fluctuate throughout the day. A linear
Exercise 15. equation that represents the price of stock for Shipment Express is y = 15 – 1.5x
