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 70 chirps in one minute and a temperature of 59.6°f.

Explanation:

Step1: Recall the formula for residual

The formula for the residual is \( \text{Residual}=y - \hat{y}\), where \(y\) is the observed value and \(\hat{y}\) is the predicted value.

Step2: Identify the observed and predicted values

The observed value \(y = 59.6\) (the given temperature). From the line of best - fit, when \(x = 70\) (chirps per minute), the predicted value \(\hat{y}=57\)

Step3: Calculate the residual

Substitute the values into the formula: \( \text{Residual}=59.6 - 57\)

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Answer:

\(2.6\)