Question

16-E1. What type of statistical interval would be relevant to informing the following questions?

1. You have a regression model of house values on several variables, including area of the house. You are considering extending your home by 800 sq. ft., and you are interested in assessing the increase value of your home after the renovation. Will the added value exceed the renovation costs?
2. You have a regression model of total trip times of delivery vehicles on total distance of trip, number of deliveries and so on. Payment is to be made according to the expected trip duration. In other words, the output of the regression model is used as a benchmark. A delivery driver thinks that the benchmark is too low for a particular trip. Could his assessment and your assessment both be reasonable?
3. You have a regression model of house values on a range of relevant variables. You are interested in bidding on a house and have come up with a valuation from the regression model. You are only interested in bidding if the house is a bargain. Where should you stop bidding?
4. You have a regression model for monthly telephone bills based on the number of people living in a household and their ages. It is based on a large database of households across Melbourne. You have two kids aged 12 and 17 and the regression predicts a monthly bill of $176. What bills do you expect over the coming months?
5. You have a regression model for demand for water on population size, in a moderate-sized country town. It is estimated that the population will increase by 25,000 over the next decade. What are the implications for water demand?
6. As in part (e), you have a regression model for monthly telephone bills on the number of people living in the house and their ages. It is based on a large database of families across Melbourne. You have two kids ager 12 and 17, and the regression predicts a monthly bill of $176. Your bills have been consistently running at $210 per month. Are your kids overusing the telephone?

Answer 1

Confidence intervals - CI tells you about the likely location of the true population parameter.

Prediction intervals tell you where you can expect to see the next data point sampled. The important point is that the PI tells you about the distribution of values, not the uncertainty in determining the population average.

You have a regression model of house values on several variables, including area of the house. You are considering extending your home by 800 sq. ft., and you are interested in assessing the increase value of your home after the renovation. Will the added value exceed the renovation costs?
Confidence interval - Here you are interested in knowing the true mean of the population.

You have a regression model of total trip times of delivery vehicles on total distance of trip, number of deliveries and so on. Payment is to be made according to the expected trip duration. In other words, the output of the regression model is used as a benchmark. A delivery driver thinks that the benchmark is too low for a particular trip. Could his assessment and your assessment both be reasonable?
Confidence interval - Here you are interested in knowing the true mean of the payment.

You have a regression model of house values on a range of relevant variables. You are interested in bidding on a house and have come up with a valuation from the regression model. You are only interested in bidding if the house is a bargain. Where should you stop bidding?
Confidence interval - Here you are interested in knowing the true mean of the value of the house

You have a regression model for monthly telephone bills based on the number of people living in a household and their ages. It is based on a large database of households across Melbourne. You have two kids aged 12 and 17 and the regression predicts a monthly bill of $176. What bills do you expect over the coming months?
Prediction interval - Here you are interested in knowing the range of the predicted value.

You have a regression model for demand for water on population size, in a moderate-sized country town. It is estimated that the population will increase by 25,000 over the next decade. What are the implications for water demand?
Prediction interval - Here you are interested in knowing the range of the predicted value.

As in part (e), you have a regression model for monthly telephone bills on the number of people living in the house and their ages. It is based on a large database of families across Melbourne. You have two kids ager 12 and 17, and the regression predicts a monthly bill of $176. Your bills have been consistently running at $210 per month. Are your kids overusing the telephone?
Confidence interval - Here you are interested in knowing the true mean of the bill and check if your kids are overusing it.