A runner times herself 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 mins
172 mins ~~~
161 mins
183 mins
It’s -0.997
Hmmm. I got 183, with the best-fit line being
y = 11.155251x - 6.892694
what did you get, and how?
I swear Ty you so frikin much
lol is right
.
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(•ㅅ•) <-0.997
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I apologize for the mistake! Can you please provide the data again so I can calculate it correctly?
To find how long it would take the runner to run 17 miles, we can use the concept of a line of best fit. A line of best fit is a straight line that represents the trend in the data points. It helps us make predictions by extending the line beyond the data points.
To find the line of best fit, we can use a technique called linear regression. In this case, we want to find a line that fits the given data points, with the x-axis representing miles and the y-axis representing time.
Using a spreadsheet or statistical software, you can input the data points (1, 7), (2, 16), (3, 30), (4, 35), (6, 57), (8, 75), (10, 106), and (12, 132). Then apply the linear regression function to find the equation of the line.
The equation of the line of best fit for the given data may look like this: y = 9x + 1, where y represents time (in minutes) and x represents miles.
To predict how long it would take the runner to run 17 miles, substitute x = 17 into the equation:
y = 9(17) + 1
y = 153 + 1
y ≈ 154
Therefore, we can expect the runner to take approximately 154 minutes to run 17 miles.