Final Exam Flashcards
What is backwards elimination?
An iterative variable selection procedure that starts with a model with all independent variables and considers removing an independent variable at each step.
What is the best subset?
A variable selection procedure that constructs and compares all possible models with up to a specified number of independent variables.
What is the coefficient of determination?
A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
What is the confidence interval?
An estimate of a population parameter that provides an interval believed to contain the value of the parameter at some level of confidence.
What is cross validation?
Assessment of the performance of a model on data other than the data that were used to generate the model
What is the dependent variable?
The variable that is being predicted or explained. It is denoted by y and is often referred to as the response.
What is a dummy variable?
A variable used to model the effect of categorical independent variables in a regression model; generally takes only the value zero or one.
What is estimated regression?
The estimate of the regression equation developed from sample data by using the least squares method.
What is the experimental region?
The range of values for the independent variables , ,…, for the data that are used to estimate the regression model.
What is extrapoltation?
Prediction of the mean value of the dependent variable y for values of the independent variables , ,…, that are outside the experimental range.
What is forward selection?
An iterative variable selection procedure that starts with a model with no variables and considers adding an independent variable at each step.
What is the holdout method?
Method of cross-validation in which sample data are randomly divided into mutually exclusive and collectively exhaustive sets, then one set is used to build the candidate models and the other set is used to compare model performances and ultimately select a model.
What is hypothesis testing?
The process of making a conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture.
What are independent variables?
The variable(s) used for predicting or explaining values of the dependent variable. It is denoted by x and is often referred to as the predictor variable.
What is Interaction?
Regression modeling technique used when the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.
What is interval estimation?
The use of sample data to calculate a range of values that is believed to include the unknown value of a population parameter.
What is a knot?
The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model; also called the breakpoint or the joint.
What is the least squares method?
A procedure for using sample data to find the estimated regression equation.
What is multicollinearity?
The degree of correlation among independent variables in a regression model.
What is linear regression?
Regression analysis in which relationships between the independent variables and the dependent variable are approximated by a straight line
What is multiple linear regression?
Regression analysis involving one dependent variable and more than one independent variable.
What is overfitting?
Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population.
What is the p-value?
The probability that a random sample of the same size collected from the same population using the same procedure will yield stronger evidence against a hypothesis than the evidence in the sample data given that the hypothesis is actually true.
What is the parameter?
A measurable factor that defines a characteristic of a population, process, or system.
What is the piecewise linear regression model?
Regression model in which one linear relationship between the independent and dependent variables is fit for values of the independent variable below a prespecified value of the independent variable, a different linear relationship between the independent and dependent variables is fit for values of the independent variable above the prespecified value of the independent variable, and the two regressions have the same estimated value of the dependent variable (i.e., are joined) at the prespecified value of the independent variable.
What is the prediction interval?
An interval estimate of the prediction of an individual y value given values of the independent variables.
What is an autoregressive model?
A regression model in which a regression relationship based on past time series values is used to predict the future time series values.
What are casual models?
Forecasting methods that relate a time series to other variables that are believed to explain or cause its behavior.
What is a cyclical pattern?
The component of the time series that results in periodic above-trend and below-trend behavior of the time series lasting more than one year.
What is exponential smoothing?
A forecasting technique that uses a weighted average of past time series values as the forecast.
What is a forecast error?
The amount by which the forecasted value differs from the observed value , denoted by .
What are forecasts?
A prediction of future values of a time series.
What is the mean absolute error?
A measure of forecasting accuracy; the average of the values of the forecast errors. Also referred to as mean absolute deviation (MAD).
What is the mean absolute percentage error?
A measure of the accuracy of a forecasting method; the average of the absolute values of the errors as a percentage of the corresponding forecast values.
What is the mean squared error?
A measure of the accuracy of a forecasting method; the average of the sum of the squared differences between the forecast values and the actual time series values.
What is the moving average method?
A method of forecasting or smoothing a time series that uses the average of the most recent n data values in the time series as the forecast for the next period.
What is the naïve forecasting method?
A forecasting technique that uses the value of the time series from the most recent period as the forecast for the current period.
What is the smoothing constant?
A parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value.
What is the stationary time series?
A time series whose statistical properties are independent of time.
What is a seasonal pattern?
The component of the time series that shows a periodic pattern over one year or less.
What is a trend?
The long-run shift or movement in the time series observable over several periods of time.
What is a time series?
A set of observations on a variable measured at successive points in time or over successive periods of time.
binding constraint
A constraint that holds as an equality at the optimal solution.
Alternative optimal solutions
The case in which more than one solution provides the optimal value for the objective function.
What are constraints?
Restrictions that limit the settings of the decision variables.
What are decision variables?
a controllable input for a linear programming model
What is the extreme point?
Graphically speaking, the feasible solution points occurring at the vertices, or “corners,” of the feasible region. With two-variable problems, extreme points are determined by the intersection of the constraint lines.
What is the feasible region?
the set of all feasible solutions
What is the feasible solution?
A solution that satisfies all the constraints simultaneously.
What is infeasiblity?
The situation in which no solution to the linear programming problem satisfies all the constraints.
What is the linear function?
A mathematical function in which each variable appears in a separate term and is raised to the first power.
What is a linear programming model (linear program)?
A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables.
What is a mathematical model?
A representation of a problem in which the objective and all constraint conditions are described by mathematical expressions.
What are non-negativity constraints?
A set of constraints that requires all variables to be nonnegative.
What is an objective function?
The expression that defines the quantity to be maximized or minimized in a linear programming model.
What is problem formulation?
The process of translating a verbal statement of a problem into a mathematical statement called the mathematical model.
Objective function coefficient allowable increase (decrease)
The allowable increase/decrease of an objective function coefficient is the amount the coefficient may increase (decrease) without causing any change in the values of the decision variables in the optimal solution. The allowable increase/decrease for the objective function coefficients can be used to calculate the range of optimality.
What is the reduced cost?
If a variable is at its lower bound of zero, the reduced cost is equal to the shadow price of the nonnegativity constraint for that variable. In general, if a variable is at its lower or upper bound, the reduced cost is the shadow price for that simple lower- or upper-bound constraint.
Right-hand side allowable increase (decrease)
The amount the right-hand side may increase (decrease) without causing any change in the shadow price for that constraint. The allowable increase and decrease for the right-hand side can be used to calculate the range of feasibility for that constraint.
What is sensitivity analysis?
The study of how changes in the input parameters of a linear programming problem affect the optimal solution.
What is the shadow price?
The change in the optimal objective function value per unit increase in the right-hand side of a constraint.
What is slack?
The difference between the right-hand-side and the left-hand-side of a less-than-or-equal-to constraint.
What is the slack variable?
A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resources.
What is the surplus variable?
A variable subtracted from the left-hand side of a greater-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level.
What is “unbounded”?
The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints.
Set objective?
Max/Min cell
What goes into the changing variable box?
Decision variables
How do you find the range of feasibility?
How much the final value of the constraints can increase and decrease before it changes
What will be the shadow price for a nonbinding constraint?
0
What is the optimal solution?
The values that produced the max profit or min
What is the objective function value?
The max profit of the optimal solution
What is the slack value for a binding constraint?
0
What is the range of optimality?
How much the objective coefficient can increase and decrease by before it changes
What is a nonbinding constraint?
When the LHS does NOT equal the RHS
Linear programming problems always involve either maximizing or minimizing an objective function.
T
What is NOT true about a linear programming problem?
A linear programming problem always has a unique optimal solution
What are the components of a linear programming model?
A linear programming problem can have more than one optimal solution.
It is possible that a linear programming problem has no optimal solution.
Sometimes a linear programming problem has an unbounded solution.
Linear programming problems can be formulated both algebraically and on spreadsheets
T
An example of a decision variable in a linear programming problem is profit maximization.
F. Objective function does this
The term BLANK refers to the expression that defines the quantity to be maximized or minimized in a linear programming model.
Objective function
The best feasible solution is called the optimal solution.
T
The optimal solution to a linear program can be found at which point of the feasible region?
An extreme point
What are some questions that are answered by sensitivity analysis?
If the right-hand side value of a constraint changes, will the objective function value change?
Over what range can a constraint’s right-hand side value without the constraint’s dual price possibly changing?
By how much will the objective function value change if a decision variable’s coefficient in the objective function changes within the range of optimality?
What does sensitivity analysis NOT answer?
By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
What does the feasible region include?
interior points.
boundary points
points at which at least one of the decision variables is zero.
What does the feasible region NOT include?
points which violate at least one of the functional or non-negativity constraints.
The effect of deleting a linear constraint from a linear programming model depends on whether or not that constraint:
is binding
The study of how changes in the input parameters of a linear programming problem affect the optimal solution is known as
sensitivity analysis
The graphical method can handle problems that involve any number of decision variables.
F
What are the problem formulation guidelines?
Understand the problem
Describe objective
Describe each constraint
Define the decisional variables
Write the objective in terms of the decision variables
Write the constraints in terms of the decision variables
What are the three types of feasible solutions?
Interior point
Extreme/corner point
Boundary point
What is the interior point?
any point inside the feasible region
What is the extreme/corner point?
the points that restrict the region from “leaving” or continuing. Country entry points
What is a boundary point?
points along the border
What is a redundant constraint?
whether you take out a constraint, the region is the same regardless
What is a location point called in the transportation problem?
Node
What are starting nodes?
supply/source/origin nodes
What are ending nodes?
demand/destination nodes
What do the lines represent in the transportation problem?
ARCS = # OF DECISION VARIABLES
