Modern Business Statistics with Microsoft Excel (MindTap Course List)
Modern Business Statistics with Microsoft Excel (MindTap Course List)
5th Edition
ISBN: 9781285433301
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Publisher: Cengage Learning
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Chapter 16.1, Problem 3E

a.

To determine

Decide whether there appears a linear relationship between x and y.

b.

To determine

Construct the estimated regression equation that relates x and y.

c.

To determine

Plot the standardized residual versus the y^ for the estimated regression equation developed.

Explain whether the model assumptions appear to be satisfied.

d.

To determine

Perform a logarithmic transformation on the variable y.

Construct the estimated regression equation using the transformed dependent variable.

Decide whether the model assumptions appear to be satisfied using the transformed dependent variable.

Explain whether a reciprocal transformation works better in this case.

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
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