Question

The manager of a water park collects data on daily high temperature and the number of customers entering the park for 15 summer week days. Based on these data he produces a least regression equation y= -3110+51.2x. One day the high temperature was 93F and 1700 customers entered the park. Which of the following is the residual for this observation?

Answer 1

Answer: A residual is the difference between the observed value of a dependent variable and the predicted value based on a given model. In this case, the manager of the water park has produced a least squares regression equation of the form y = -3110 + 51.2x, where y is the number of customers entering the park and x is the daily high temperature. This equation can be used to predict the number of customers based on a given temperature.

On the day in question, the high temperature was 93F and 1700 customers entered the park. Using the given equation, we can predict the number of customers that would be expected based on this temperature:

y = -3110 + 51.2x

= -3110 + 51.2 * 93

= -3110 + 4768.6

= 1658.6

The residual for this observation is the difference between the observed value of 1700 and the predicted value of 1658.6, which is 1700 - 1658.6 = 41.4. This is the residual for this observation.