Explain the difference between Prediction Interval and Confidence Interval with application based examples.

Prediction Interval is used to predict the next single response where Confidence Interval is used to predict the average of multiple responses. Due to this the Prediction Interval will have a larger range than the Confidence Interval.

Prediction interval is used for expressing a range of possible outcomes for a single event, based on observed process variation.  Confidence interval is used for expressing a range of possible outcomes averaged over time.  Because a prediction interval contains a single data point, it will always be greater than a confidence interval for a given variable of interest.

 

A practical example would be an estimate of how long it takes me to commute to my office on a daily basis (average, therefore confidence interval) versus an estimate of how long it might take to commute on a given day when I have an important appointment that I can't be late to.

 

 

Explain the difference between Prediction Interval and Confidence Interval with application based examples.

Prediction interval is relative to the individual values and will be larger than the confidence interval (more variation)

Confidence Interval is relative to the average values

 

If a we created a regression line model that depicted the probability of failure

a) if asked what is the interval of failure on the next unit we would use the prediction interval

b) if asked what is the interval of the average failures for tomorrow, we would use the confidence interval

c) if asked what is the precise probability of x failure the we would use the regression line as the point estimate

 

The confidence interval is in for the range of response over time, while the prediction interval is for a particular / single event.

A confidence interval is used to predict the average value of a random variable, whereas a prediction interval is used to predict an individual value.  Since the variation in the average of random variable is less than that of the random variable itself, a confidence interval is narrower than a prediction interval.  My golf handicap is calculated based on my average scores over a number of rounds.  I will usually shoot close to my handicap, but on any particular day, I could shoot much better, or much worse.

A confidence interval is a range of values that will contain a parameter assumed to be non-random. A prediction interval is associated with a random variable with a specific probability of that variable lying within the interval. Prediction intervals are confidence intervals for predictions derived from regression models. Prediction intervals are always wider than the confidence intervals of equal percentage. 

 

For example, if you have data for how many cigarettes a person smokes per day as the independent variable and the number of years they lived as the dependent variable, the life expectancy of people who smoke 10 cigarettes per day will fall within the tighter tolerances of the confidence interval. The life expectancy of a single person who smokes 10 cigarettes per day will fall within the wider prediction interval.

Confidence intervals provides a range for the mean.

Prediction intervals provides a range for a single new observation.

The prediction interval is wider than the confidence interval because it includes the uncertainty of individual measures, i.e. data scatter.

For example, LeBron averaged between 23.7 and 35.3 points per game (ppg) across the 13 years he has been in the playoffs.  But he has scored over 30 points in 110 of his 238 playoff games, which illustrates a broader scatter for his points in any individual game.