# Statistics Problem Set: Regression and Linear Programming

6. A multiple regression analysis including 50 data points and 5 independent variables results in 40. The multiple standard error of estimate will be:

a. 0.901

b. 0.888

c. 0.800

d. 0.953

e. 0.894

4. Sampling error is evident when:

a. a question is poorly worded

b. the sample is too small

c. the sample is not random

d. the sample mean differs from the population mean

When using exponential smoothing, if you want the forecast to react quickly to movements in the series, you should choose:

a. values of alpha near 1

b. values of alpha near 0

c. values of alpha midway between 0 and 1

d. it depends on the data set

9. Consider the following linear programming problem:

Maximize 2x_1 + 4x_2

Subject to

x_1 + x_2 <= 5

-x_1 + x_2 >= 8

x_1, x_2 >= 0

The above linear programming problem:

a. has only one optimal solution

b. has more than one optimal solution

c. exhibits infeasibility

d. exhibits unboundedness

10. The expected value of perfect information (EVPI) is equal to:

a. EMV with posterior information - EMV with prior information

b. EMV with free perfect information - EMV with information

c. EMV with free perfect information - EMV with no information

d. EMV with perfect information - EMV with less than perfect information

Please answer the following True or False:

a. Assume that the histogram of a data set is symmetric and bell shaped, with a mean of 75 and standard deviation of 10. Then, approximately 95% of the data values were between 55 and 95.

b. A low p-value provides evidence for accepting the null hypothesis and rejecting the alternative.

c. A t-test is used to determine whether the coefficients of the regression model are significantly different from zero.

d. Decision trees are more appropriate tools than decision tables when a sequence of decisions must be made.

e. If a solution to an LP problem satisfies all of the constraints, then is must be feasible and bounded.

f. Correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship.

g. In multiple regression, the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression, since the F-test combines these t-tests into a single test.

h. In a random walk model, there are significantly more runs than expected, and the autocorrelations are not

significant.

i. When we maximize or minimize the value of a decision variable by running several simulations simultaneously, we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.

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#### Solution Preview

Hi there,

Thanks for letting me work on your post. I've attached my detailed explanation in the word document.

Thanks.

Tony

__________________________________________

6. A multiple regression analysis including 50 data points and 5 independent variables results in 40. The multiple standard error of estimate will be:

SE=sqrt(sum/(n-k-1))=sqrt(40/(50-5-1))=0.9534, therefore, d is the right choice.

d. 0.953

4. Sampling error is evident when:

One of the efficient approaches to reduce sampling error is randomness. Therefore, c is the right choice.

c. the sample is not random

When using exponential smoothing, if you want the forecast to react quickly to movements in the series, you should choose:

If a rapid response to a real change in the pattern of observations is desired, a large value of alpha is appropriate. Therefore, a is the right choice.

a. values of alpha near 1

9. Since the two ...

#### Solution Summary

The following posting helps with problems involving regression and linear programming.

Mean, mode, frequency distribution, normal distribution, Excel, scatter diagram, simple regression analysis, multiple regression analysis, regression analysis, linear programming

1 What is a mean? A median? A mode?

2 What is a frequency distribution?

3 What is a normal distribution?

4 What is the approximate probability that a data point will fall within one standard deviation of the mean of a normally distributed data set?

5 How does one begin to use Excel (or other comparable software) to calculate basic statistics on a set of input data?

6 How does one use Excel (or other comparable software) to calculate and display a scatter diagram?

7 What is linear regression? What is the difference between simple regression analysis and multiple regression analysis?

8 What is the most important concept in regression analysis?

9 What are the limitations of regression analysis?

10 What is linear programming? What are the two major types of linear programming problems?

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