Question

question a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. calculate the residual for the data point that corresponds to 64 chirps in one minute and a temperature of 56.8°f.

Explanation:

Step1: Find regression line equation

Use points $(64,56)$ and $(104,66)$.
Slope: $m=\frac{66-56}{104-64}=\frac{10}{40}=0.25$
Equation: $y - 56 = 0.25(x - 64)$
Simplify: $y=0.25x + 56 - 16=0.25x + 40$

Step2: Calculate predicted value

Substitute $x=64$ into the equation:
$y_{pred}=0.25(64)+40=16+40=56$

Step3: Compute residual

Residual = Observed value - Predicted value
Residual = $56.8 - 56$

Answer:

$0.8$