Question

question
jose decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches, then throws back into the water. after plotting all his data, he draws a line of best fit. calculate the residual for the data point that corresponds to 28 inches and a weight of 19.8 pounds.
(the chart shows a scatter plot with a line of best fit. the x - axis is catfish length (inches) and the y - axis is catfish weight (pounds). points on the line of best fit include (20,5), (28,21), (40,45), (42,49) etc. there is a data point at (28,19.8) approximately.)

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 the length (x) is 28 inches, the predicted weight (y) is 21 pounds (from the point (28,21) on the line).

Step3: Calculate Residual

The observed weight is 19.8 pounds. Using the residual formula:
\( \text{Residual} = 19.8 - 21 = -1.2 \)

Answer:

-1.2