QUESTIONS
Question 1
Find the linear regression line for the following table of values. You will need to use a calculator, spreadsheet, or statistical software.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 3 | 2.36 |
| 4 | 5.37 |
| 5 | 5.71 |
| 6 | 6.69 |
| 7 | 7.67 |
| 8 | 6.16 |
Question 2
Using a calculator or statistical software, find the linear regression line for the data in the table below.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 2 | 9.58 |
| 3 | 7.46 |
| 4 | 9.28 |
| 5 | 11.58 |
| 6 | 14.94 |
| 7 | 14.97 |
| 8 | 18.43 |
| 9 | 18.04 |
| 10 | 20.42 |
Question 3
How many sunny days must there be for the plants to grow 35 centimeters?
- Round your final answer to the nearest whole number.
Question 4
A park ranger is interested in plant growth around the trails of the park. He finds the plants growth, G, is dependent on the number of sunny days that occur in three months, x, and can be modeled by the function
G(x)=−8+3x.
Draw the graph of the growth function by plotting its G-intercept and another point.
Question 5
The scatter plot below shows data relating total income and the number of children a family has. Which of the following patterns does the scatter plot show?
- Positive linear pattern
- Positive linear pattern with deviations
- Negative linear pattern
- Negative linear pattern with deviations
- No pattern
Question 6
Using the linear relationship graphed above, estimate the percent of snack purchases if 80% of customers wait in line for more than 15 minutes.
Question 7
A ticket taker at a movie theater explored the relationship between the percent of customers that wait more than 15 minutes in line for tickets and the percent of customers that purchase snacks at the theater. The ticket ticker collects information from 6 lines during a particular week, shown in the table below.
Use the graph below to plot the points and develop a linear relationship between the percent of waiting customers and the percent of snack purchases at a movie theater.
| Line | % of Waiting Customers | % of Snack Purchases |
| 1 | 90 | 3 |
| 2 | 75 | 11 |
| 3 | 60 | 16 |
| 4 | 52 | 20 |
| 5 | 40 | 30 |
| 6 | 30 | 35 |
Question 8
Using the linear relationship graphed above, estimate the percent of return customers if 80% of customers wait more than 10 minutes in line.
Question 9
A grocery store manager explored the relationship between the percent of customers that wait more than 10 minutes in line and the percent of return customers at the store. The manager collects information from 6 checkout lines, shown in the table below.
Use the graph below to plot the points and develop a linear relationship between the percent of waiting customers and the percent of return customers.
| Line | % of Waiting Customers | % of Return Customers |
| 1 | 20 | 85 |
| 2 | 35 | 80 |
| 3 | 50 | 75 |
| 4 | 60 | 60 |
| 5 | 70 | 50 |
| 6 | 90 | 32 |
Question 10
How much time did a person spend at the library over a month for them to spend 40 hours reading a book?
- Round your final answer to the nearest whole number.
Question 11
A librarian finds that the number of hours spent reading a book over a month, R, is dependent on the numbers of hours a person spends at the library over the course of a month, x, and can be modeled by the function
R(x)=26+1.5x.
Draw the graph of the reading function by plotting its R-intercept and another point.
Question 12
Using a calculator or statistical software, find the linear regression line for the data in the table below.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 0 | 3.16 |
| 1 | 4.72 |
| 2 | 4.5 |
| 3 | 6.6 |
| 4 | 7.72 |
| 5 | 7.39 |
| 6 | 11.11 |
| 7 | 10.57 |
| 8 | 11.06 |
Question 13
Using a calculator or statistical software, find the linear regression line for the data in the table below.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 0 | 2.12 |
| 1 | 2.19 |
| 2 | 1.92 |
| 3 | 2.79 |
| 4 | 3.81 |
| 5 | 4.72 |
ANSWERS:
Question 1
Find the linear regression line for the following table of values. You will need to use a calculator, spreadsheet, or statistical software.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 3 | 2.36 |
| 4 | 5.37 |
| 5 | 5.71 |
| 6 | 6.69 |
| 7 | 7.67 |
| 8 | 6.16 |
Answer
y=0.77x+1.44
Question 2
Using a calculator or statistical software, find the linear regression line for the data in the table below.
Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.
| x | y |
| 2 | 9.58 |
| 3 | 7.46 |
| 4 | 9.28 |
| 5 | 11.58 |
| 6 | 14.94 |
| 7 | 14.97 |
| 8 | 18.43 |
| 9 | 18.04 |
| 10 | 20.42 |
Answer
y=1.61x+4.18
Question 3
How many sunny days must there be for the plants to grow 35 centimeters?
- Round your final answer to the nearest whole number.
Answer
14 days
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