1.5E: Exercises - Fitting Linear Models to Data
Exercise \(\PageIndex{1}\)
In Europe and Asia, m-commerce is popular. M-commerce users have special mobile phones that work like electronic wallets as well as provide phone and Internet services. Users can do everything from paying for parking to buying a TV set or soda from a machine to banking to checking sports scores on the Internet. For the years 2000 through 2004, what was the relationship between the year and the number of m-commerce users? Construct a scatter plot and find the linear regression model that best fits the data. Let \(x =\) the year and let \(y =\) the number of m-commerce users, in millions.
| \(x\) (year) | \(y\) (# of users) |
|---|---|
| 2000 | 0.5 |
| 2002 | 20.0 |
| 2003 | 33.0 |
| 2004 | 47.0 |
Exercise \(\PageIndex{2}\)
A random sample of 11 statistics students produced the following data, where \(x\) is the Unit 1 Exam score out of 80, and \(y\) is the Final Exam score out of 200.
| \(x\) (Unit 1 Exam score) | \(y\) (Final Exam score) |
|---|---|
| 65 | 151 |
| 67 | 133 |
| 71 | 185 |
| 71 | 163 |
| 66 | 126 |
| 75 | 198 |
| 67 | 153 |
| 70 | 163 |
| 71 | 159 |
| 69 | 151 |
| 69 | 159 |
A random student earned a 58 on the Unit 1 Exam. If that student follows the class trend, what would you expect this student to earn on the final exam?
Exercise \(\PageIndex{3}\)
SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table show different depths with the maximum dive times in minutes. Use your calculator to find the linear regression line and predict the maximum dive time for 110 feet.
| \(X\) (depth in feet) | \(Y\) (maximum dive time) |
|---|---|
| 50 | 80 |
| 60 | 55 |
| 70 | 45 |
| 80 | 35 |
| 90 | 25 |
| 100 | 22 |
Exercise \(\PageIndex{4}\)
Amelia plays basketball for her high school. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data. She has a goal of playing in college and needs to score 40 points in a game to be considered for the college team. Based on the trend, how many hours each week should she practice her jump shot?
| \(X\) (hours practicing jump shot) | \(Y\) (points scored in a game) |
|---|---|
| 4 | 13 |
| 6 | 18 |
| 7 | 22 |
| 9 | 27 |
| 11 | 30 |