Question

: Calculating and interpreting residuals. Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in Celsius, and the etching rate, in cm/min, of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature:

V=2t−0.5

What is the residual if the room temperature was 25°C, and the cupric chloride had an etching rate of 5 cm/min?

Answer 1

The residual is -44.5 cm/min.

Step-by-step explanation:

To calculate the residual, we can substitute the values given in the equation: V = 2t - 0.5. We are given that the room temperature (t) is 25°C and the etching rate (V) is 5 cm/min. Substituting these values into the equation, we have: 5 = 2(25) - 0.5. Solving this equation, we find that the expected etching rate at 25°C is 49.5 cm/min.

However, the actual etching rate is given as 5 cm/min. The residual is the difference between the actual value and the predicted value: 5 - 49.5 = -44.5. Therefore, the residual is -44.5 cm/min.