Use the table to answer the question.

Height Weight Line of Best Fit: y^=105x−439

5.8 175 170
5.9 188 180.5
6.0 191 191
6.08 185 199.4
6.2 210 212
6.3 235 222.5
What value point would you graph for residual at a height of 6.08 given the data in the table?

(1 point)
Responses

0
0

14.4
14.4

−14.4
negative 14.4

−14.6
negative 14.6

1 answer

To find the residual for a height of 6.08, you first need to use the equation of the line of best fit, \( y = 105x - 439 \), to determine the predicted weight at that height.

  1. Calculate the predicted weight (y) when height (x) is 6.08: \[ y = 105(6.08) - 439 \] \[ y = 638.4 - 439 \] \[ y = 199.4 \]

  2. Now, determine the actual weight from the table for a height of 6.08, which is 185.

  3. Finally, calculate the residual by subtracting the predicted weight from the actual weight: \[ \text{Residual} = \text{Actual weight} - \text{Predicted weight} \] \[ \text{Residual} = 185 - 199.4 = -14.4 \]

Thus, the value to graph for the residual at a height of 6.08 is \(-14.4\).

So the correct response is: −14.4 (negative 14.4).