# Statistics

Your company is developing a new radio communication system. Weight, power output, and frequency have each been identified by your engineering and productions staffs as being potential significant contributors to the production cost of a radio communication system. The following relationships between cost and these parameters have been hypothesized:

Cost will increase with increased radio weight.

Cost will increase with increased power output.

Cost will increase with increased frequency.

Your company collected first unit cost, weight, power output, and frequency data for fifteen radio communication systems that your company has previously manufactured. Your department head had a young summer intern who is familiar with performing linear regression using Microsoft Excel perform the following univariate and multivariate regressions using a 95% confidence interval.

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

The regression statistics developed by the intern are summarized in the accompanying Microsoft Excel spreadsheet entitled â??Radio Communication System Regression Statisticsâ?. However, the intern is not confident that he understands how to correctly interpret the regression statistics he has generated. Your department head is aware of your recently acquired expertise regarding interpreting linear regression statistics and has tasked you to analyze the regression statistics generated by the intern and answer the following:

11) Identify each of the following as either being a dependent variable, an independent variable, or not a variable.

a) Weight

b) Power

c) Cost

d) Frequency

e) System

12) Which of the following regression models fails to satisfy the common sense test criteria regarding the hypothesized correlation between the dependent variable and independent variable? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) All of the above

e) None of the above

13) Which of the following regression models fails to satisfy the common sense test criteria regarding the statistical significance of the model as a whole? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

14) Which of the following regression models fails to satisfy the common sense test criteria regarding the statistical significance of the strength of the relationship between the dependent variable and the independent variable(s)? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

15) Which of the following models evidences the least probability of the observed R2 or Adjusted R2 values for the linear regression model being attributable to random chance as opposed to being attributable to an actual linear relationship existing between the dependent and independent variable(s)? (select one)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

16) Which of the following regression models explain less than 50% of the observed variation between the actual values of the dependent variable and the mean value of the dependent variable values for the sample data set? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

h) None of the above

17) Which of the following regression models would result in the largest degree of error on average when using the model to predict the first unit cost for a new communication system? (select one)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

18) Which of the following regression models satisfy the requirement for the F-significance value associated with the model being less than or equal to the specified 0.05 statistical significance criterion? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

h) All of the above

19) Which of the following regression models satisfy the requirement for the p-value associated with each independent variable associated with the model being less than or equal to the specified 0.05 statistical significance criterion? (select all that apply)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

20) Which of the following regression models evidences the strongest relationship between the dependent variable and the independent variable(s)? (select one)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

21) Which of the following regression models is the preferred regression model? (select one)

a) Cost vs. Weight

b) Cost vs. Power

c) Cost vs. Frequency

d) Cost vs. Weight and Power

e) Cost vs. Weight and Frequency

f) Cost vs. Power and Frequency

g) Cost vs. Weight, Power and Frequency

https://brainmass.com/statistics/multivariate-anova/statistics-356128

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.

Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]

having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).

Demonstrate that the mle theta;hat is a sufficient statistic for theta;.

Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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