A runner times her to see how long it takes her to run different distances. The table shows the runner's times (in minutes) for running several distances (in miles).
Miles| 1 | 2 | 3 | 4 | 6 | 8 | 10 | 12|
Time | 7|16|30|35|57|75|106|132|
About how long would you expect it to take this runner to run 17 miles? Find a line of best fit for this data and use it to make your prediction.
205 minutes
172 minutes
161 minutes
183 minutes
I have grid paper right by me, I've been trying for a little now, but I don't know if I'm doing the whole line of best fit thing right...
Its 183.
Plot your points.
To find the line of best fit you try to do the following things
1) Use a ruler to see where the line fits (you try for about half the points above the line and half the points below the line).
2) See if your ruler will hit two points while getting half the points above the line and half below.
Let me know where you think the line goes (through which points)
I plotted your points...
So I have a line of best fit in mind.
It "may" be very similar to your line.
Let me know two points your line goes through : )
Study this video
https://www.youtube.com/watch?v=ugmhjwAQDIE
Here is another, a bit less boring in its presentation:
https://www.youtube.com/watch?v=DmGLQkUm-4g
Keep in mind that this is an approximation, so not every
student in the class would necessarily have the same result
My line has 4 over 1 under and went through 3 of my dots I placed on, and I went upwards diagonally
To find a line of best fit for the given data, we will use linear regression. Linear regression helps us find the equation of a line that best represents the relationship between two variables.
Here's how you can find the line of best fit for this data:
1. Start by plotting the given data points on the grid paper, with the miles on the x-axis and the time on the y-axis.
2. Once you have plotted the points, draw a straight line that closely fits the overall trend of the data. Ensure that you try to include as many data points as possible, while still maintaining the overall fit.
3. Now, using a ruler, draw the line of best fit that passes through the plotted points. The line should represent the overall trend of the data.
4. Once you have drawn the line, extend it on the grid to intersect with the x-axis (miles) at the desired value of 17 miles.
5. Next, look at the point where the extended line intersects the y-axis (time). This point represents the predicted time for running 17 miles.
6. Read the corresponding value on the y-axis to determine the predicted time.
Based on the line of best fit, it seems like the predicted time for running 17 miles would be approximately 161 minutes.
Note: The line of best fit is an estimation based on the given data points and is not guaranteed to be completely accurate for all values.
If you are having trouble finding the line of best fit manually, you can also use spreadsheet software, such as Excel or Google Sheets, to perform linear regression and calculate the predicted time for running 17 miles with greater accuracy.