In: Statistics and Probability
16-E1. What type of statistical interval would be relevant to informing the following questions?
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.