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Chapter 13: Problem 6

Briefly explain the difference between a deterministic and a probabilistic regression model.

Short Answer

Expert verified
Deterministic regression models give a fixed output for a given input without accounting for any variability and uncertainty, while probabilistic regression models treat output as random variables and provide a range of outcomes with corresponding probabilities.

Step by step solution

01

Define deterministic regression models

A deterministic regression model is a type of model where the output is precisely determined through certain mathematical computations from a set of specific inputs. There are no random elements involved in the process, which means for a given input, the model will always produce the same output.
02

Define probabilistic regression models

In contrast, a probabilistic regression model works differently. With this type of model, the output is not fixed even for a specific input. Various outputs can be produced for the same input and each output is associated with a certain probability. In other words, output in this model is treated as random variables rather than fixed quantities.
03

Comparing the two models

The key difference between these two types of regression models is therefore the way they handle variability and uncertainty. Deterministic models provide a specific output for a given set of inputs, ignoring any potential randomness or variations. Probabilistic regression models, on the other hand, consider uncertainty by treating output as random variables, thereby providing a range of possible outcomes with corresponding probabilities.

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Most popular questions from this chapter

The recommended air pressure in a basketball is between 7 and 9 pounds per square inch (psi). When dropped from a height of 6 feet, a properly inflated basketball should bounce upward between 52 and 56 inches (http://www.bestsoccerbuys.com/balls-basketball.html). The basketball coach at a local high school purchased 10 new basketballs for the upcoming season, inflated the balls to pressures between 7 and \(9 \mathrm{psi}\), and performed the bounce test mentioned above. The data obtained are given in the following table. $$ \begin{array}{l|rrrrrrrrrr} \hline \text { Pressure (psi) } & 7.8 & 8.1 & 8.3 & 7.4 & 8.9 & 7.2 & 8.6 & 7.5 & 8.1 & 8.5 \\ \hline \text { Bounce height (inches) } & 54.1 & 54.3 & 55.2 & 53.3 & 55.4 & 52.2 & 55.7 & 54.6 & 54.8 & 55.3 \\ \hline \end{array} $$ a. With the pressure as an independent variable and bounce height as a dependent variable, compute \(\mathrm{SS}_{x x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x y}\) b. Find the least squares regression line. c. Interpret the meaning of the values of \(a\) and \(b\) calculated in part \(\mathrm{b}\). d. Calculate \(r\) and \(r^{2}\) and explain what they mean. e. Compute the standard deviation of errors. f. Predict the bounce height of a basketball for \(x=8.0\). g. Construct a \(98 \%\) confidence interval for \(B\). h. Test at a \(5 \%\) significance level whether \(B\) is different from zero. i. Using \(\alpha=.05\), can you conclude that \(\rho\) is different from zero?

A sample data set produced the following information. $$ \begin{aligned} &n=12, \quad \Sigma x=66, \quad \Sigma y=588, \quad \Sigma x y=2244, \\ &\Sigma x^{2}=396, \quad \text { and } \quad \Sigma y^{2}=58,734 \end{aligned} $$ a. Calculate the linear correlation coefficient \(r .\) b. Using a \(1 \%\) significance level, can you conclude that \(\rho\) is negative?

Briefly explain the assumptions of the population regression model.

Explain the meaning of coefficient of determination.

Explain the following. a. Population regression line b. Sample regression line c. True values of \(A\) and \(B\) d. Estimated values of \(A\) and \(B\) that are denoted by \(a\) and \(b\), respectively
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