Question

The main difference between linear (LP) and nonlinear programming problems (NLP) is that

	a.	No interaction terms are allowed in NLP
	b.	NLP must have a nonlinear objective function
	c.	Only one constraint in NLP can be nonlinear
	d.	Some constraints in NLP may be nonlinear

The standard prediction error is

	a.	always smaller than the standard error.
	b.	used to construct confidence intervals for predicted values.
	c.	measures the variability in the predicted values.
	d.	all of these.

The GRG algorithm terminates when it

	a.	has reached the global optimal solution.
	b.	has completed 100 iterations.
	c.	when it detects no feasible direction for improvement.
	d.	when it reaches the steepest gradient.

The regression function indicates the

	a.	average value the dependent variable assumes for a given value of the independent variable.
	b.	average value the dependent variable assumes for a given value of the dependent variable
	c.	actual value the dependent variable assumes for a given value of the independent variable
	d.	actual value the independent variable assumes for a given value of the dependent variable

Which of the following is an advantage of using the TREND() function versus the regression tool?

	a.	The TREND() function handles multiple dependent variable data.
	b.	The TREND() function does not use a least squares regression line.
	c.	The TREND() function provides more statistical information.
	d.	The TREND() function is dynamically updated when input to the function changes.

Answer 1

1. Answer : D (Some Constraints in NLP may be non-linear)

Rationale : In NLP, either the objective function or the constraints ( one or more than one) are non-linear). It might be possible that the objective function is linear and the constraints are non-linear or vice-versa.

2. Answer : D (All of these)

Rationale : Standard prediction error is used to measure the accuracy of the predictions, i.e., the variability in the predicted values. Just like standard error, standard prediction error is used to construct the confidence intervals for the predicted values.

Also, the standard prediction error is always smaller than standard error. It is represented by formula:

SPE =

where SPE = standard prediction error

SE = standard error

R = Correlation between dependent and independent variable ( r is smaller than 1)

3. Answer : C (When it detects no feasible direction for improvement)

Rationale : GRG algorithm is used by solver to solve NLP problems. It initiates at any feasible solution and moves in feasible region to improve the objective function and terminates when there is no feasible direction for improvement.

4. Answer : A (Average value of the dependent variable assumes for a given value of the independent variable)

Rationale: The regression model can not predict the true or actual values. It takes into account the independent and dependent variables and forms a regression equation indicating the relationship of dependent variable with independent variable or simple words, indicates the value of dependent value for a given value of independent variable.

5. Answer : D (The trend () function is dynamically updated when input to the function changes)

Rationale : Unlike regression model, trend () function is not able to provide more statistical information. Also, it computes least sqaure linear regression line. The only advantage of trend () function over regression is that it is dynamically updated when any input to the function changes.