Confidence and Prediction Bounds in Regression  -- Explain how engineering decision-making is effected by the use of confidence and prediction bounds in regression analysis. Don't just describe how to calculate the bounds. Use your knowledge of statistics to discuss the actual impact these factors have on our engineering.

 

In engineering, a variety of intervals are used to characterize the results and the most well known of these are confidence intervals. A confidence interval refers to a range of values which are derived from sample statistics, that is likely to contain the value of an unknown population parameter although the confidence intervals are not always appropriate. we take a look at the different types of intervals that are available in Minitab, the confidence interval calculations usually take sample data and produce a range of values that are likely to contain the population parameter that you are interested in. For example, the confidence interval of the mean. 

The primary purpose of regression in data is prediction. A prediction interval is a type of confidence interval that you can use with predictions from linear and nonlinear models. A prediction interval refers to a range which is likely to contain the response value of a single new observation given specified settings of the predictors in your model.

The performance confidence is usually influenced by physical properties of the stimulus in which a decision is based on. For example, evidence quality favoring a decision ,it impacts the accuracy and reaction times, in which it has been shown to affect confidence, therefore establishing an internally generated feedback-signal.

The prediction interval is always wider than the corresponding confidence interval of the prediction. This is due to the added uncertainty which is involved in predicting a single response versus the mean response. The prediction interval usually helps to predict in what range a future individual observation will fall, while a confidence interval indicates the likely range of values which are associated with some statistical parameter of the data for example the population mean.