x = miles run y = Wt in lbs

Question

10 130
1 200
3 167
5 145
8 135
The line of best fit for this data set is y = 195 - 7.3x. Find the weight of a cheetah that runs 7 miles and state whether extrapolation or interpolation

Answer 1

To find the weight of a cheetah that runs 7 miles using the line of best fit \( y = 195 - 7.3x \):

1. Substitute \( x = 7 \) into the equation: \[ y = 195 - 7.3 \times 7 \]

2. Calculate: \[ y = 195 - 51.1 \] \[ y = 143.9 \]

Therefore, the estimated weight of a cheetah that runs 7 miles is approximately 143.9 lbs.

Since the value of 7 miles is outside the range of the given data set (the highest value is 10 miles and the lowest is 1 mile), this calculation involves extrapolation. Extrapolation is used when predicting values outside the range of the observed data.