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 = 4 + 0.07(number of sunny days). find and interpret the residual for an average orange volume of 8 cubic inches in a season with 46 sunny days. the residual is \boxed{}. (type an integer or a decimal.)

Explanation:

Step1: Recall residual formula

Residual = Observed value - Predicted value.

Step2: Find predicted volume

Given the line of best - fit equation \( \text{volume}=4 + 0.07(\text{number of sunny days}) \). For 46 sunny days, substitute the number of sunny days into the equation:
\( \text{Predicted volume}=4+0.07\times46 \)
First, calculate \( 0.07\times46 = 3.22 \), then \( 4 + 3.22=7.22 \).

Step3: Calculate residual

The observed volume is 8 cubic inches. Using the residual formula:
\( \text{Residual}=8 - 7.22 = 0.78 \)

Answer:

0.78