Question

Prediction Interval Using the heights and weights described in Exercise 1, a height of 180 cm is used to find that the predicted weight is 91.3 kg, and the 95% prediction interval is (59.0 kg, 123.6 kg). Write a statement that interprets that prediction interval. What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.3 kg? Why is the terminology of prediction interval used instead of confidence interval?

Short answer

The 95% prediction interval stands for the fact that for thegiven value of height (x) at 180 cm, there is 95% confidence that the predicted value of weight (y) will fall between 59.0 kg and 123.6 kg.

The advantage of the prediction interval over the point estimate of y is that it tells the accuracy of the prediction. It considers the margin of error (likely to occur) when predicting the weight for a given height.

Since the interval estimate is used to define the predicted value of the response variable and not any of its parameters (mean, variance, proportion, etc.), the computed interval is called the prediction interval and not the confidence interval.

Step-by-step solution

Given information

The 95% prediction interval for the weight of males (y) for a height (x) of 180 cm is (59.0 kg, 123.6 kg).

Prediction interval

A prediction interval is the interval estimate of the predicted value of the response variable for a given value of the predictor variable.

Here, the 95% prediction interval of the weight of males when the height is 180 cm is obtained as (59.0 kg, 123.6 kg).

This means that there is a 95% confidence that the predicted value of the weight will fall within 59.0 kg and 123.6 kg when the height is 180 cm.

Advantage of using a prediction interval instead of using only the predicted weight of 91.3 kg

An interval estimate has the advantage of defining a range with a known probability of capturing the desired value.

Here, it is better to define a prediction interval than a simple estimate because the prediction interval provides some accuracy in the fact that the predicted value of the weight will lie between 59.0 kg and 123.6 kg and not pinpoint just a single value.

The prediction interval allows you to be more cautious in the interpretation of data and assists in maintaining the right perspective.

Prediction interval versus confidence interval

A confidence interval is used to define the range within which the value of a parameter is likely to fall.For example, a 95% confidence interval can be constructed to define a set of values that will include the slope coefficient.

On the other hand, a prediction interval is used to define the range within which the value of the response variable is likely to fall.

It is given that the 95% prediction interval for the value of the weight of males when the height is 180 cm is (59.0 kg, 123.6 kg). Thus, it would be incorrect to call it a confidence interval because it is not used to define the value of a parameter.