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 78 chirps in one minute and a temperature of 61.6°f.

Explanation:

Step1: Define residual formula

Residual = Observed $y$ - Predicted $y$

Step2: Find predicted temperature

Use line points $(93,66)$ and $(90,65)$ to find slope:
$\text{Slope } m = \frac{66-65}{93-90} = \frac{1}{3}$
Equation: $y - 65 = \frac{1}{3}(x - 90)$
Simplify: $y = \frac{1}{3}x + 35$
For $x=78$:
$y_{\text{predicted}} = \frac{1}{3}(78) + 35 = 26 + 35 = 61.6$

Step3: Calculate residual

Observed $y=61$, Predicted $y=61.6$
$\text{Residual} = 61 - 61.6 = -0.6$

Answer:

$-0.6^\circ\text{F}$