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# Statistics

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Statistics
1. The general form of the multiple regression equation is the following:

y = a + b1x1 + b2x2 + b3x3 + ..... + bnxn

"a" is the intercept value defined as the value of y (dependent variable) if all independent variables are equal to zero
"b1" is the sensitivity of y to variable x1. If x1 is varied by 1 unit, y will vary by b1 units
"b2" is the sensitivity of y to variable x2. If x2 is varied by 1 unit, y will vary by b2 units
"b3" is the sensitivity of y to variable x3. If x3 is varied by 1 unit, y will vary by b2 units

Why the coefficients of the independent variable b1, b2 are called sensitivity coefficients?

International Finance

2. What is your opinion of the alternative goal of the firm, to balance the interests of the shareholders and the stakeholders? Do you agree with this view? Why or Why not?

3. A fancy way of saying the difference in yield or interest rates for a bond that will mature in perhaps 30 years versus a bond that will mature in 10 years or 1 year. You can create a graph to show this difference.

With this in mind, please do research on the internet and post the yield to maturity for a 1 year US Treasury Bond, a 10 year US Treasury Bond. Then find the yield to maturity for comparable Gilt. Gilts are the name for UK Government bonds. So you would locate the yield for a 1 year Gilt and a 10 year Gilt.

4. It is hard to believe a competitor is a stakeholder. Isn't the goal of competition to win and perhaps even dominate the market? If so, how can a company have an interest in the ongoing health of their competitors (except to beat them?) How is a competitor a stakeholder?

#### Solution Preview

1. The general form of the multiple regression equation is the following:

y = a + b1x1 + b2x2 + b3x3 + ..... + bnxn

"a" is the intercept value defined as the value of y (dependent variable) if all independent variables are equal to zero
"b1" is the sensitivity of y to variable x1. If x1 is varied by 1 unit, y will vary by b1 units
"b2" is the sensitivity of y to variable x2. If x2 is varied by 1 unit, y will vary by b2 units
"b3" is the sensitivity of y to variable x3. If x3 is varied by 1 unit, y will vary by b2 units

Why the coefficients of the independent variable b1, b2 are called sensitivity coefficients?

The coefficients of the independent variable b1, b2 are called sensitivity coefficients because of the fact that these are subject to change the direction in which the study is conducted. For example, if b1 is about the environment, b2 is the drug, and b3 is the diagnosis. All are subject to change based off the conditions and the type of drug that is administered with the affects that can occur from giving it to the participant. This is why they are sensitivity coefficients because each of them can change based on the situation and the individual, which in turn can impact the results for each of them that take part in the study based off their reaction to the drug.
...

#### Solution Summary

This solution discussed statistics and international finance.

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## 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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