Question

calculate residual from context (catfish)
this is the only question in this section.
question
bao decides to research the relationship between the length in inches and the weight of a certain species of catfish. she measures the length and weight of a number of specimens she catches, then throws back into the water. after plotting all her data, she draws a line of best fit. calculate the residual for the data point that corresponds to 24 inches and a weight of 17 pounds.
(chart: catfish length (inches) on x - axis, catfish weight (pounds) on y - axis. line of best fit with points (20,5), (24,14), (28,23) and data points plotted.)

Explanation:

Step1: Recall Residual Formula

Residual is calculated as \( \text{Residual} = \text{Observed Value} - \text{Predicted Value} \).

Step2: Find Predicted Value

From the line of best fit, when \( x = 24 \) (length in inches), the predicted weight \( \hat{y} \) is 14 pounds (from the point \((24, 14)\) on the line).

Step3: Identify Observed Value

The observed weight (actual value) for \( x = 24 \) is 17 pounds.

Step4: Calculate Residual

Using the formula: \( \text{Residual} = 17 - 14 = 3 \).

Answer:

3