Use the table to answer the question.

Question

This table displays height vs. weight with line of best fit for given data
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

14.4
14.4

−14.6
negative 14.6

−14.4
negative 14.4

0

Answer 1

To find the residual for a given height, you need to calculate the difference between the actual weight and the weight predicted by the line of best fit at that height.

1. Find the predicted weight at a height of 6.08 using the line of best fit equation: \[ \hat{y} = 105(6.08) - 439 \]

   Calculate \(105 \times 6.08\): \[ 105 \times 6.08 = 638.4 \]

   Now subtract 439: \[ 638.4 - 439 = 199.4 \]

   So, the predicted weight (\(\hat{y}\)) at a height of 6.08 is 199.4.

2. Identify the actual weight at a height of 6.08 from the table: From the table, the actual weight at 6.08 is 185.

3. Calculate the residual: Residual = Actual weight - Predicted weight \[ \text{Residual} = 185 - 199.4 = -14.4 \]

Thus, the value point you would graph for the residual at a height of 6.08 is −14.4.