Question

over the years, a farmer has collected data on the average volume of the oranges in his crop in cubic inches based on the number of sunny days in the 120 - day growing season. the equation of the line of best - fit is volume = 2+0.07(number of sunny days). find and interpret the residual for an average orange volume of 6 cubic inches in a season with 49 sunny days.
the residual is \square. (type an integer or a decimal.)

Explanation:

Step1: Calculate predicted volume

Substitute sunny days = 49 into the line of best fit:
$\text{Predicted Volume} = 2 + 0.07 \times 49$
$\text{Predicted Volume} = 2 + 3.43 = 5.43$

Step2: Compute the residual

Residual = Observed value - Predicted value
$\text{Residual} = 6 - 5.43$

Answer:

0.57

Interpretation: The residual of 0.57 means the observed average orange volume is 0.57 cubic inches higher than the volume predicted by the line of best fit for a season with 49 sunny days.