Let the predictor variable x represent heights of males and let response variable y represent weights of males. A sample of 153 heights and weights results in s Subscript eequals16.75064 cm. Using the regression found from the data, a height of 185 cm is used to find that the predicted weight is 91.4 kg and the 95% prediction interval is (58.2 kg comma 124.6 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 91.4 kg? Why is the terminology of prediction interval used instead of confidence interval?

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Step-by-step explanation:

- Write a statement that interprets that prediction interval.

The prediction interval (58.2 kg, 124.6 kg) represents the range of values that the true predicted weight for a height of 185 cm using the regression obtained from the data can actually, possibly take on to a certain level of confidence.

- What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.4 kg?

The prediction interval is better to use instead of just using a predicted weight because in computing the prediction interval, we consider all the factors, biases and significant factors that can introduce uncertainties into the regression used to just find the predicted weight.

So, the prediction interval is more encompassing and has a better chance of containing the true weight that corresponds to the height 185 cm because it incorporates so many things thay can go wrong with the regression into its computation unlike the predicted weight.

- Why is the terminology of prediction interval used instead of confidence interval?

This is because the interval is obtained from the regression results, used in predicting weights, given height.

Confidence interval is used for numerical distributions to estimate the interval of range of values where the true population mean can be found with a certain level of confidence.

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