To calculate the residual at a height of 6.08, we need to follow these steps:
-
Determine the actual weight at a height of 6.08: From the table, the actual weight at a height of 6.08 is 185.
-
Determine the predicted weight using the line of best fit: We can use the equation of the line of best fit, \(y = 105x - 439\), where \(x\) is the height (6.08 in this case).
Substituting \(x = 6.08\):
\[ y = 105(6.08) - 439 \]
\[ y = 638.4 - 439 \]
\[ y = 199.4 \]
Therefore, the predicted weight at a height of 6.08 is 199.4.
-
Calculate the residual: The residual is found by subtracting the predicted value from the actual value:
\[ \text{Residual} = \text{Actual Weight} - \text{Predicted Weight} \]
\[ \text{Residual} = 185 - 199.4 = -14.4 \]
Thus, the value for the residual at a height of 6.08 is −14.4.