The maintenance of swimming pools is quite costly because of all the chlorine that is needed to keep the water clear and relatively free of germs.

A chain of hotels (all with outdoor pools) seeking to reduce costs decided to analyze the factors that determine how much chlorine is needed. They commissioned a chemist to conduct an analysis. It is believed that the speed at which chlorine in a pool is depleted is dependent on the temperature of the water (higher temperature uses chlorine faster); pH level, which is a measure of the acidity of the water (pH ranges from 0 to 14, where 0 is very acidic and 14 is very alkaline; levels around 7.5 use the least chlorine); and weather (sunshine uses up chlorine). The chemist conducted the following experiment. The percentage of chlorine depletion during 8-hour days was recorded under varying conditions of pH level, water temperature, and weather conditions.

These data were recorded in the following way:

Column 1: Percentage of chlorine depletion over 8 hours

Column 2: Temperature (degrees Fahrenheit)

Column 3: pH level

Column 4: 1 = Mainly cloudy, 2 = Sunny, 3 = Partly sunny

a. Write the equation of the model that you would suggest.

b. Use regression analysis to estimate the model's coefficients.

c. Test to determine whether the model is valid.

d. Can we infer that higher temperatures deplete chlorine more quickly?

e. Is there evidence to infer that the belief about the relationship between chlorine depletion and pH level is correct?

f. Can we infer that weather is a factor in chlorine depletion?