8.04 Lines of best fit
The following scatter plot shows the data for two variables, x and y:
Sketch the line of best fit for this data.
Use your line of best fit to estimate the value of y when:
x = 4.5
x = 9
The following scatter plot graphs data for the number of people in a room and the room temperature collected by a researcher.
Sketch the line of best fit for this data.
Use your line of best fit to estimate the room temperature when there are:
35 people in the room
100 people in the room
The following scatter plot graphs data for the number of copies of a particular book sold at various prices:
Sketch the line of best fit for this data.
Use your line of best fit to find the number of books that will be sold when the price is:
\$33
\$18
The following scatter plot graphs data for the number of copies of a particular book sold at various prices.
Sketch the line of best fit for this data.
Use the line of best fit to find the number of books that will be sold when the price is:
\$33
\$18
Is the relationship between the price of the book and the number of copies sold positive or negative?
The following scatter plot graphs data for the number of ice blocks sold at a shop on days with different temperatures.
Sketch the line of best fit for this data.
Use your answer line of best fit to estimate the number of ice blocks that will be sold on a:
88 \degree \text{F} day
108 \degree \text{F} day
Does the number of ice blocks sold increase or decrease as the temperature increases?
The following scatter plot graphs data for the number of balls hit and the number of runs scored by a batsman:
Sketch the line of best fit for this data.
Use the line of best fit to estimate the number of runs scored by the batsman after hitting:
27 balls
66 balls
Is the relationship between the two variables positive or negative?
The average monthly temperature and the average wind speed, in knots, in a particular location was plotted over several months. The graph shows the points for each month’s data and their line of best fit:
Use the line of best fit to approximate the wind speed on a day when the temperature is 41\degree \text{F}.
Consider the following scatter plot:
Is the relationship between the x and y variables positive or negative?
Sketch the line of best fit for this data.
Which of the following could be the equation for the line of best fit:
A dam used to supply water to the neighboring town had the following data recorded for its volume over a number of months:
| \text{Month} | 1 | 2 | 3 | 4 |
| \text{Volume (billion of liters)} | 116 | 106 | 104 | 92 |
Plot the data on a coordinate plane.
Sketch the line of best fit for this data.
Jordano measures his heart rate at various times while running. The data is shown below in the table:
| \text{Time (minutes)} | 0 | 2 | 4 | 6 | 8 | 10 |
| \text{Heart Rate (BPM)} | 58 | 54 | 58 | 67 | 67 | 74 |
Plot the data and sketch the line of best fit.
Which data point is closest to the line of best fit?
Which data point is furthest from the line of best fit?
The number of fish in a river is measured over a five year period:
| \text{Time in years}\, (t\text{)} | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Number of fish } (F\text{)} | 1903 | 1994 | 1995 | 1602 | 1695 | 1311 |
The data has been graphed along with a line of best fit:
Predict the number of years until there are no fish left in the river.
Predict the number of fish remaining in the river after 7 years.
According to the line of best fit, how many years are there until there are 900 fish left in the river?
Scientists conducted a study to see people's reaction times after they've had different amounts of sleep. The results are recorded in the table:
| \text{Number of hours of sleep} \left(x\right) | 1.1 | 1.5 | 2.1 | 2.5 | 3.5 | 4 |
|---|---|---|---|---|---|---|
| \text{Reaction time in seconds} \left(y\right) | 4.66 | 4.1 | 4.66 | 3.7 | 3.6 | 3.4 |
The data has been graphed along with a line of best fit:
Predict the reaction time for someone who has slept for 5 hours.
Predict the number of hours someone sleeps if they have a reaction time of 4 seconds.
Chirping crickets can be an excellent indication on how hot or cool it is outside. Different species of crickets have different chirping rates but for a particular species the following data was recorded:
| \text{Number of chirps per minute} | 77 | 115 | 150 | 176 |
|---|---|---|---|---|
| \text{Temperature } (\degree \text{F}) | 57 | 63 | 70 | 75 |
What is the temperature when the crickets make 140 chirps each minute?
How many chirps per minute will the crickets make if the temperature is 71\degree \text{F}?
How many chirps are the crickets making each minute if the temperature is 66\degree \text{F}?
A plane's altitude (A) is measured at several times (t) during its descent:
| \text{Time } (t \text{ seconds}) | 0 | 200 | 400 | 1700 |
|---|---|---|---|---|
| \text{Altitude } (A \text{ ft}) | 27\,000 | 25\,639 | 23\,267 | 1945 |
The data has been graphed along with a line of best fit:
Predict the altitude of the plane 600 seconds into the descent.
Predict the altitude of the plane 900 seconds into the descent.
For how many seconds has the plane been descending when it is at an altitude of 17\,00 feet?
How many seconds did the plane take to descend to the ground?
The number of hours spent watching TV each evening, h, is measured against the percentage results, m, achieved in the Economics exam. The line of best fit for the resulting data is shown:
Explain what the y-intercept represents.
Does the interpretation in the previous part make sense in this context? Explain your answer.
Would it be reasonable to use the line of best fit to predict average grade of students who watch more than 10 hours of TV?
The heights (in inches) and the weights (in pounds) of 8 primary school children is shown on the scattergraph below.
State the y-value of the y-intercept.
Explain the meaning of y-intercept in this context.
Does the interpretation in the previous part make sense in this context? Explain your answer.
Given that the data points are all between 40 and 60 \text{ in} of height, is the fitted line appropriate for heights of 10 to 20\text{ in}?
The average number of pages read to a child each day and the child’s growing vocabulary are measured.
| Pages read per day | 25 | 27 | 29 | 3 | 13 | 31 | 18 | 29 | 29 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|
| Total vocabulary | 402 | 440 | 467 | 76 | 220 | 487 | 295 | 457 | 460 | 106 |
The data has been graphed along with a line of best fit.
State the y-intercept.
Interpret the meaning of the y-intercept.
Does the interpretation in the previous part make sense in this context?
Could we use the line of best fit to predict a child's vocabulary if they read more than 500 pages per day?
Concern over student use of the social media app SnappyChatty leads to a study of student grades in Mathematics versus minutes spent using the app.
| Time (minutes) | 292 | 153 | 354 | 253 | 11 | 42 | 195 | 7 | 162 | 254 |
|---|---|---|---|---|---|---|---|---|---|---|
| Grade | 26 | 63 | 13 | 37 | 97 | 89 | 51 | 98 | 59 | 36 |
The data has been graphed along with a line of best fit.
State the y-intercept, correct to the nearest ten.
Interpret the meaning of the y-intercept.
Does the interpretation in the previous part make sense in this context?
Could we use the line of best fit to predict a student's grade if they spent more than 400 minutes using SnappyChatty?
The following scattergraph shows the value of various 4 bedroom, 2 bathroom homes in a new suburb:
State the y-intercept.
Explain what the y-intercept represents.
Does the interpretation in the previous part make sense in this context? Explain your answer.
Use the graph to estimate the age of a house with an average value of \$2\,000\,000. Give your answer in years to one decimal place.
Use the graph to estimate the average price of a house with age 3 years.
The price of various second-hand Mitsubishi Lancers are shown in the table below:
| \text{Age} | 1 | 2 | 0 | 5 | 7 | 4 | 3 | 4 | 8 | 2 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Value} \\ \text{(in thousands of dollars)} | 16 | 13 | 21.99 | 10 | 8.6 | 12.5 | 11 | 11 | 4.5 | 14.5 |
The line of best fit for the data is shown below:
State the y-intercept to the nearest thousand.
Explain what the y-intercept represents.
Does the interpretation in the previous part make sense in this context? Explain your answer.
At what age, to the nearest year, would a car be worth \$0?
Can we use this line of best fit to find the value of a car that is older than 11 years? Explain your answer.