Draw an approximate line of best fit by hand for each of the the scatter plots below:
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 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 5\degree \text{C}.
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:
Consider the following scatter plot:
Is the relationship between the x and y variables positive or negative?
Which of the following could be the equation for the line of best fit:
Use technology to find the line of best fit for the sets of data below. Write the equation with the coefficient and constant term to the nearest two decimal places.
| x | 24 | 37 | 19 | 31 | 32 | 22 | 14 | 30 | 23 | 40 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | -7 | -8 | -3 | -6 | -9 | -8 | -2 | -8 | -8 | -12 |
| x | 7 | 18 | 16 | 9 | 16 | 19 | 8 | 8 | 12 | 7 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 16.29 | 3.56 | 7.25 | 12.11 | 8.25 | 3.26 | 12.5 | 12.5 | 10.33 | 14.29 |
| x | 44 | 39 | 41 | 50 | 45 | 55 | 48 | 54 | 44 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 2.29 | 1.57 | 3.86 | 3.14 | 4.43 | 4.86 | 3.86 | 4.71 | 4.29 | 4.14 |
Several cars underwent a brake test and their age, x (in years), was measured against their stopping distance, y (in metres). The scatter plot shows the results and a line of best fit that approximates the positive correlation:
According to the line, what is the stopping distance of a car that is 6 years old?
According to the line, what is the stopping distance of a car that is 10 years old?
Using the information found above, determine the gradient of the line of best fit.
State the value of the vertical intercept of the line.
Use the line of best fit found to estimate the stopping distance of a car that is 4.5 years old.
The distance of several locations from the equator and their temperature on a particular day is measured. The values are presented on the following scatter plot:
Determine whether the following could be the equation of the line relating distance \left(x\right) and temperature \left(y\right):
Estimate the distance from the equator, x, if the temperature is 30.59 \degree \text{C}.
Find the equation of the line of best fit on the scatter plot shown:
Consider the scatter plot shown:
Find the equation of the line of best fit.
Use the line of best fit to approximate the value of y for x = 6.9.
A car company looked at the relationship between how much it had spent on advertising and the amount of sales each month over several months. The data has been plotted on the scatter graph and a line of best fit drawn:
Two points on the line are \left(3200, 300\right) and \left(5600, 450\right). Find the gradient of the line of best fit.
The line of best fit can be written in the form S=mA+ c, where m is the gradient, c is the vertical intercept, S is the money spent on sales in thousands of dollars, and A is the advertising costs.
Determine the value of c, the vertical intercept of the line.
Use the line of best fit to estimate the number of sales next month if \$4800 is to be spent on advertising.