QTM 2 REVIEW FOR FINAL
How to calculate VIF
1 / (1-R^2)
A third-order autoregressive model is fitted to an annual time series with 24 values. The estimated parameters are b0=3.50, b1=1.10, b2=0.90, b3=0.35, and the three most recent observed values are Y22=17, Y23=30, and Y24=43. Forecast the value for the next year. (Y25)
= 3.5 + (43*1.1) + (30*.9) + (17*.35) =b0 + (Y24*b1) + (Y23*b2) + (Y22*b3)
Determining the worst payoff for each alternative and choosing the alternative with the best worst is called: A. minimin. B. maximin. C. maximax. D. minimax.
B. maximin.
Which of the following is not an advantage of exponential smoothing? A. It enables you to smooth out cyclical components. B. It enables you to smooth out seasonal components. C. It enables you to perform more than one-period ahead forecasting. D. It enables you to perform one-period ahead forecasting.
C. It enables you to perform more than one-period ahead forecasting.
When is a dummy variable used as an independent variable in a regression model? A. It is used when 2 independent variables interact. B. It is used when a curvilinear relationship is suspected. C. It is used when the variable involved is categorical. D. It is used when the variable involved is numerical.
C. It is used when the variable involved is categorical.
An independent variable Xj is considered highly correlated with the other independent variables if which of these expressions is true? A. VIFj>VIFi for i≠j B. VIFj<VIFi for i≠j C. VIFj>5 D. VIFj<5
C. VIFj>5
The term opportunity loss is most closely related to: A. maximin regret. B. maximax regret. C. minimax regret. D. minimin regret.
C. minimax regret.
Which of the following could be a valid objective function in a linear programming problem, where X, Y, and Z are relevant variables or functions? A. Min: (X + Y) / Z B. Max: Z = 5X2 + 2Y2 C. Max: 3X + 3Y + (1/3)Z D. Max: Z = 5XY
C. Max: 3X + 3Y + (1/3)Z
What is true when testing for normality of errors? A. Errors are normally distributed when the scatter diagram shows a straight-line distribution. B. A scatter diagram of the whole data is always used to verify normality. C. It is easier to evaluate normality with small sample sizes. D. Normality is verified by inspecting for a bell-shaped distribution.
D. Normality is verified by inspecting for a bell-shaped distribution.
What is the standard error of the estimate a measure of? A. The total variation of the Y variable B. The explained variation C. The variation of the X variable D. The variation around the sample regression line
D. The variation around the sample regression line
The optimal solution to a linear programming model that has been solved using the graphical approach: A. must be above and the right of all constraint lines. B. must be below and on the left side of all constraint lines. C. is typically located at the origin. D. is typically at a corner of the feasible region.
D. is typically at a corner of the feasible region.
Decision variables: A. measure the values of each constraint. B. measure the objective function. C. always exist for each constraint. D. measure how much or how many items to produce, purchase, hire, etc.
D. measure how much or how many items to produce, purchase, hire, etc.
In order for an optimization problem to have multiple optimal solutions: A. two or more of the constraints must have the same slope. B. two or more of the constraints must not have intersection points. C. the objective function and one constraint must have the same y-intercept. D. the objective function and one constraint must have the same slope.
D. the objective function and one constraint must have the same slope.
In a linear programming problem, if a given resource has not been fully used, we can conclude that the shadow price associated with that resource: A. could have a positive, negative or a value of zero. (no sign restrictions). B. will have a negative value. C. will have a positive value. D. will have a value of zero.
D. will have a value of zero.
Perform a residual analysis - minitab
Do stat, regression, regression, in storage hit residuals. to find mad of residuals, hit calc, then type in mean(abs('RESI')) and store in a new column
Of last 3 models (Linear Trend, Quadratic Trend, and Exponential Smoothed), select the one that you consider to be the most accurate, and explain the reasoning for your choice. Do you also expect it to be the best model for prediction? Why?
Exponential Smoothed is the most accurate. The reason for this is because it has the lowest mean absolute percentage error at 11, and the lowest mean absolute deviation with 366. We did expect this to be the most accurate of the models, as unlike simple trendlines, exponential smoothing lines place more weight on the most recent data to give you the most accurate predictions as to what is to come in the future. Also, exponential smoothing is best utilized when the data isn't seasonal or cyclical, which is true for the data we analyzed. Undoubtedly, this is the best model to use for the data set.
Random numbers used in a simulation should be normally distributed and efficiently generated. True False
False
multiple regression
Is the model statistically significant ("better than nothing")? Why? Yes it's significant because the F value is super high What is the explanatory power of this model? r^2 =95.2 Adjusted r^2 value would be a good model if you're adding in the interaction term
Midterm 1
Questions
MIDTERM 3
REVIEW
Midterm 2
Review
If you are using exponential smoothing for forecasting an annual time series of revenues, what is your forecast for next year if the smoothed value for this year is $32.4 million?
The forecast for next year is $32.432.4 million. (Type an integer or a decimal.)
Which of the following regression procedures are needed when the dependent variable is categorical? a)Use logistic regression in lieu of least squares regression. b)Use a dummy variable to represent the dependent variable. c)Evaluate alternate models using best subsets regression. d)Evaluate interaction and quadratic terms.
a)use logistic regression in lieu of least squares regression
What do we mean when we say that a sample linear regression model is "statistically" useful? a)The model is an excellent predictor of Y. b)The model is "practically" useful for predicting Y. c)The model is a better predictor of Y than "nothing" (i.e., a simple constant). Your answer is correct. d)All the statistics computed from the sample make sense.
c) the model is a better predictor of y than "nothing"
Which of the following will not change a nonlinear model into a linear model? a)logarithmic transformation b)quadratic regression model c)square-root transformation d)variance inflationary factor
d) variance inflationary factor
confidence interval for slope
first, find t value by doing b1/sb1. then for confidence interval, go to minitab, hit graph, prob distribution plot, view probability, for a t distribution, d.f. = n-k-1 (n-2), 95% = in shaded area write .05 probability and hit both tails, hit ok. get 2.12 as value from the graph (on bottom). then do 2.12 * 1.2(standard error sb1) to get margin of error(me). confidence interval lower limit = 5.44- (2.12*1.2) (b1-me) and 5.44+(2.12*1.2) the upper limit.
expected opportunity loss
make a regret table and multiply each value for the decision by its probability best solution is the one with the lowest EOL
Which of the following statements about moving averages is not true? A. It can be used to smooth a series. B. It gives greater weight to more recent data. C. It gives equal weight to all values in the computation. D. It is simpler than the method of exponential smoothing.
B. It gives greater weight to more recent data.
Determine if the statement is true or false. Collinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables. True False
False
Decision criteria that are used for decision-making when probabilities are known include: A. Expected opportunity loss B. Equal likelihood C. Maximin D. None of the above
A. Expected opportunity loss
In a multiple regression model, which of the following is correct regarding the value of the adjusted r2? A. It has to be positive. B. It can be larger than 1. C. It can be negative. D. It has to be larger than the coefficient of multiple determination.
A. It has to be positive.
Fill in the blank: ________ is a technique for selecting numbers randomly from a probability distribution. A. Monte Carlo B. Monaco C. Analogue simulation D. Marseille
A. Monte Carlo
Which of the following is used to find a "best" model? A. Mallow's Cp B. Odds ratio C. SST D. Standard error of the estimate
A. Mallow's Cp
If the plot of the residuals is fan shaped, which assumption is violated? A. No assumptions are violated; the graph should resemble a fan B. Homoscedasticity C. Normality D. Independence of errors
B. Homoscedasticity
Fill in the blank: ________ numbers are numbers derived from a mathematical process that appear to be random. A. Randomized B. Pseudorandom C. Random D. Semi-random
B. Pseudorandom
The Hurwicz criterion is a compromise: A. None of these B. between the maximax and maximin criteria. C. between the maximin and minimax criteria. D. between the minimax and maximax criteria.
B. between the maximax and maximin criteria.
In solving a minimization problem graphically, the optimal solution is at the extreme point ________ the origin. A. exactly at B. closest to C. farthest from D. parallel to
B. closest to
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending. What should the microeconomist who developed this multiple regression model be particularly concerned with? A. Normality of residuals B. Missing observations C. Collinearity D. Randomness of error terms
C. Collinearity
Unlike decision models, simulation ordinarily provides which of the following: A. recommendations B. suggestions C. operating characteristics D. solutions
C. operating characteristics
Decision criteria that are used for decision-making when probabilities are known include: A. Maximax B. Minimax regret C. Maximin D. All of the above E. None of the above
E. None of the above
In Excel the VLOOKUP function is used to determine values for continuous random variables. True False
FALSE
time series plot
Generate a plot of the time series, using Stat > Time Series > Time Series Plot. To label the axis, use the Time/Scale option: set the Calendar option to "Quarter Year" and the Start Values to Quarter 1, Year 2011. Plot the time series, using Stat > Time Series > Time Series Plot. Note that you can use the Year column as the x-axis labels by selecting the Time/Scale... option, choosing Stamp, and selecting the Year column for the Stamp. Compare the accuracy of the Regression model result (standard error) to the appropriate accuracy measure of the Trend Analysis result (RMSE = MSD ). Compare the ratio of the two measures to the ratio n/(n-2) where n is the number of observations. This relationship will always hold when comparing an MSD to an equivalent standard error of regression. (2) Standard Error of the Regression Model is 735.427 MSDis 693.367 Ratio of Two Measures: (735.427/693.367)=1.0607 n/(n-2)=18/(18-2)=1.0607
Interpret the meaning of a logistic regression slope coefficient equal to 0.8.
Holding constant the effect of other variables, the natural logarithm of the estimated odds ratio for the dependent categorical response will increase by a mean of 0.8 for each unit increase in the independent variable to which the coefficient corresponds.
Interpret the meaning of the p-value.
The p-value is the probability of getting an overall test statistic equal to or greater than the sample result, assuming there is no linear relationship between the dependent variable and the independent variables.
time series autoregression
minitab : regression, do expanded tables and hit durbin watson statistic for unusal values. also hit stat, time series, lag, series is dependendant variable, do lag 1. then, do that two more times. then, hit regression and put dpendent variable in and then put all 3 lags in continuous variables section. if not significant, delete lag3 and so on...
modeling, best subsets
models that satisfy the Cp requirement (which is Cp ≤ k + 1). Of the highlighted rows, set the text color of largest R-sq(adj) red. The set the text color of the smallest S red. Those are the criteria for selecting the best model Out of all these highlighted values, look for value with the lowest standard error and highest adj. r^2 value If collinearity is observed, delete the variable with the largest VIF and re-run the Best Subsets analysis.
If SSR=63 and SST=84, compute the coefficient of determination, r2, and interpret its meaning. r2=. 75.75 (Type an integer or a decimal. Do not round.) What is the meaning of r2? A. r2 of the variation in the independent variable can be explained by the variation in the dependent variable. B. r2•100% of the variation in the dependent variable can be explained by the variation in the independent variable. Your answer is correct. C. 1−r2 of the variation in the dependent variable cannot be explained by the variation in the independent variable. D. 1−r2•100% of the variation in the independent variable cannot be explained by the variation in the dependent variable.
r2=.75 Equation:(SSR/SST) B. r2•100% of the variation in the dependent variable can be explained by the variation in the independent variable.
linear regression explanations
the p-value of the regression and both independent variables (Alcohol and Chlorides) are both below the alpha of 0.05. Therefore, we can claim the data is statistically significant and therefore can look into the explanatory power (Adjusted R squared and Standard Error). The Adjusted R Squared value takes into account multiple independent variables, and means that 40.09% of the variation in wine quality can be explained by variation in the two independent variables, alcohol and chlorides. This means the model is not the strongest in terms of explanatory power with regards to R squared adjusted (for the two independent variables). R^2, which can also be used for explanatory power but doesn't change based on "k," is 42.54%. Standard error predicts the accuracy of the regression model, or how accurate the model predicts the observed values. With a standard error of 0.8846, this means that the sample mean is likely to be 0.8846 units away from the true population mean (68% of the data lies between 0.8846 units).
Which of the following methods should not be used for short-term forecasts into the future? A. Moving averages B. Autoregressive modeling C. Exponential smoothing D. Linear trend model
A. Moving averages
What does the coefficient of determination (r2) tell you? A. The proportion of total variation that is explained B. That the coefficient of correlation (r) is larger than 1 C. Whether r has any significance D. That you should not partition the total variation
A. The proportion of total variation that is explained
While checking for linearity by examining the residual plot, what must be true of the residuals? A. They must be randomly scattered. B. They must form a parabolic shape. C. They must be below the x-axis. D. They must exhibit a linear trend.
A. They must be randomly scattered.
You need to decide whether you should invest in a particular stock. You would like to invest if the price is likely to rise in the long run. You have data on the daily mean price of this stock over the past 12 months. What is your best action? A. estimate a least square trend model B. compute the MAD statistic C. perform exponential smoothing D. compute moving averages
A. estimate a least square trend model
What is the minimum expected opportunity loss also equal to? A. expected value of perfect information B. expected profit under certainty C. expected value under certainty minus the expected monetary value of the worst alternative D. coefficient of variation
A. expected value of perfect information
In solving a maximization problem graphically, the optimal solution is at the extreme point ________ the origin. A. farthest from B. exactly at C. parallel to D. closest to
A. farthest from
The region that satisfies all of the constraints in a graphical linear programming problem is called the: A. feasible solution space. B. region of non-negativity. C. region of optimality. D. optimal solution space.
A. feasible solution space.
A common limitation of simulation is that: A. model building is costly and time-consuming. B. models are typically well-structured and can be developed only for problems that are also well-structured. C. it is more difficult to manipulate the elements of a computer simulation than the actual system. D. it is usually possible to realistically validate simulation results.
A. model building is costly and time-consuming.
Why is the method of least squares used on time-series data? A. obtaining the trend equation B. deseasonalizing the data C. exponentially smoothing a series D. eliminating irregular movements
A. obtaining the trend equation
To assess the adequacy of a forecasting model, what is a measure that is often used? A. the MAD B. exponential smoothing C. moving averages D. quadratic trend analysis
A. the MAD
A shadow price reflects which of the following in a maximization problem? A. the marginal gain in the objective that would be realized by adding one unit of a resource B. the marginal gain in the objective of selling one more unit C. the marginal gain in the objective that would be realized by subtracting one unit of a resource D. the marginal cost of adding additional resources
A. the marginal gain in the objective that would be realized by adding one unit of a resource
What is the method of moving averages used for? A. to smooth a series B. in regression analysis C. to plot a series D. to exponentiate a series
A. to smooth a series
Pseudorandom numbers exhibit a ________ in order to be considered truly random. A. uniform distribution B. detectable run of certain numbers C. limited number of possible outcomes D. detectable pattern
A. uniform distribution
For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________. A. improvement, resource B. increase, parameter C. decrease, resource D. decrease, parameter
A. improvement, resource
A seasonal regression model was fit to quarterly sales data (in $10,000) for a small company specializing in green cleaning products. The results are shown below. What is the forecast (in $10,000) for the second quarter of the next year? The regression equation is Sales=136−31.0 Q1−52.0 Q2−51.2 Q3 Predictor Coef SE Coef T P Constant 136.167 4.822 28.24 0.000 Q1 −31.000 6.820 −4.55 0.000 Q2 −52.000 6.820 −7.62 0.000 Q3 −51.167 6.820 −7.50 0.000 S=11.8121 R-Sq=79.3% R-Sq(adj)=76.2% A. 136 B. 84 C. 105 D. 52
B. 84
Decision criteria that are used for decision-making when probabilities are known include: A. Equal likelihood B. Expected opportunity loss C. Maximin D. None of the above
B. Expected opportunity loss
________ is not part of a Monte Carlo simulation. A. Evaluating the results B. Finding an optimal solution C. Analyzing results D. Analyzing results
B. Finding an optimal solution
When can an interaction term in a multiple regression model be used? A. It can be used when neither one of 2 independent variables contribute significantly to the regression model. B. It can be used when the relationship between X1 and Y changes for differing values of X2. C. It can be used when there is a curvilinear relationship between the dependent and independent variables. D. It can be used when the coefficient of determination is small.
B. It can be used when the relationship between X1 and Y changes for differing values of X2.
A decision-making situation can include several components, including states of nature. In this context, the most appropriate characterization of this term is: A. States of nature are probabilities of events. B. States of nature are events that may occur in the future, over which the decision-maker has no control. C. States of nature are future natural conditions such as weather. D. States of nature are the potential outcomes of decision choices.
B. States of nature are events that may occur in the future, over which the decision-maker has no control.
What do the residuals represent? A. The square root of the slope B. The difference between the actual Y values and the predicted Y values C. The difference between the actual Y values and the mean of Y D. The predicted value of Y for the average X value
B. The difference between the actual Y values and the predicted Y values
A marketing manager has developed a regression model to predict quarterly sales of his company's down jackets based on price and amount spent on advertising. An intern suggests that he include an indicator (dummy) variable for the fall quarter. a) How would you code such a variable? (What values would it have for each quarter?) b) Why does the intern's suggestion make sense? a) How would the fall variable be coded? A. spring=2, summer=3, fall=0, winter=1 B. spring=0, summer=0, fall=1, winter=0 C. spring=1, summer=2, fall=3, winter=4 D. spring=3, summer=4, fall=1, winter=2 b) Why does the intern's suggestion make sense? A. There is probably a seasonal cycle in the sales of jackets would be modeled well by an indicator variable for fall. B. Sales of jackets are probably higher in the fall quarter than in other quarters. C. The company probably spends more on advertising in the fall, so the indicator variable will capture that behavior. D. The suggestion does not make sense. The variation with fall would be captured by the linear regression model already.
B. spring=0, summer=0, fall=1, winter=0 B. Sales of jackets are probably higher in the fall quarter than in other quarters.
For a resource constraint, either its slack value must be ________ or its shadow price must be ________. A. zero, negative B. zero, zero C. negative, negative D. negative, zero
B. zero, zero
Which of the following could not be a linear programming problem constraint? A. 1A + 2B ≤ 3 B. 1A + 2B = 3 C. 1A + 2B ≠ 3 D. 1A + 2B ≥ 3
C. 1A + 2B ≠ 3
In a linear programming problem, the binding constraints for the optimal solution are: 5 X1 + 3 X2 ≤ 30 2 X1 + 5 X2 ≤ 20 Which of these objective functions will lead to multiple optimal solutions? A. 2 X1 + 1 X2 B. 7 X1 + 8 X2 C. 25 X1 + 15 X2 D. 80 X1 + 60
C. 25 X1 + 15 X2
Which of the following statements about the method of exponential smoothing is not true? A. It uses all earlier observations in each smoothing calculation. B. It can be used for forecasting. C. It gives greater weight to the earlier observations in the series. D. It gives greater weight to more recent data.
C. It gives greater weight to the earlier observations in the series.
What does the Variance Inflationary Factor (VIF) measure? A. The standard deviation of the slope B. The contribution of each X variable with the Y variable after all other X variables are included in the model C. The correlation of the X variables with each other D. The correlation of the X variables with the Y variable
C. The correlation of the X variables with each other
Which of these statements is true when using exponential smoothing for purposes of forecasting? A. The next smoothed value becomes the forecast. B. The previous smoothed value becomes the forecast. C. The current smoothed value becomes the forecast. D. None of the above
C. The current smoothed value becomes the forecast.
What does the slope (b1) represent? A. The variation around the line of regression B. The predicted value of Y C. The estimated average change in Y per unit change in X D. The predicted value of Y when X=0
C. The estimated average change in Y per unit change in X
How do you interpret a coefficient of determination, r2, equal to 0.01? Choose the correct answer below. A. The interpretation is that 99% of the variation in the independent variable can be explained by the variation in the dependent variable. B. The interpretation is that 0.01% of the variation in the independent variable can be explained by the variation in the dependent variable. C. The interpretation is that 1% of the variation in the dependent variable can be explained by the variation in the independent variable. D. The interpretation is that 0.99% of the variation in the dependent variable can be explained by the variation in the independent variable.
C. The interpretation is that 1% of the variation in the dependent variable can be explained by the variation in the independent variable.
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X)-measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model Yi=β0+β1Xi+εi. The results of the simple linear regression are provided below. Y=−2,700+20X, SYX=65, two-tail p value=0.034 (for testing β1) Interpret the estimate of β0, the Y-intercept of the line. A. For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700. B. All companies will be charged at least $2,700 by the bank. C. There is no practical interpretation since a sales revenue of $0 is a nonsensical value. D. About 95% of the observed service charges fall within $2,700 of the least squares line.
C. There is no practical interpretation since a sales revenue of $0 is a nonsensical value.
In a linear maximization problem, the constraint on gruyere cheese is binding. If the original amount of the cheese is 4 lbs. and the allowable range for cheese is from 3 lbs. to 6 lbs., decreasing the amount of cheese by 2 lb. will result in which of the following outcomes: A. different product mix, same total profit as before. B. same product mix, different total profit. C. different product mix, different total profit. D. same product mix, same total profit. E. cannot be determined from the information given.
C. different product mix, different total profit.
A seed value is a(n): A. analytic solution of a simulation experiment. B. steady state solution of a simulation experiment. C. number used to start a sequence of random numbers. D. first run of a simulation model.
C. number used to start a sequence of random numbers.
A plant manager wants to find a production schedule that maximizes profit, when a constraint on machine time is binding. The original amount of machine time available is 200 minutes., and the allowable range of machine time is from 130 minutes to 300 minutes. If the manager can provide 1 additional machine hour, it will result in: A. different product mix, different total profit. B. different product mix, same total profit as before. C. same product mix, different total profit. D. same product mix, same total profit. E. cannot be determined from the information given.
C. same product mix, different total profit.
In a linear maximization problem, the constraint on gruyere cheese is binding. If the original amount of the cheese is 4 lbs. and the allowable range for cheese is from 3 lbs. to 6 lbs., increasing the amount of cheese by 1 lb. will result in which of the following outcomes: A. different product mix, different total profit. B. different product mix, same total profit as before. C. same product mix, different total profit. D. same product mix, same total profit. E. cannot be determined from the information given.
C. same product mix, different total profit.
Develop a seasonal regression-based forecasting equation for Sales as a function of time (T) and a categorical factor for Quarter. Make sure that Q1 is your base level. Insert your Model Summary and Coefficient Table here.
Construct an autoregression model for Hain's Sales.. Start with a 4th-order AR model, and determine the best order to use. Lag 4 is not significant, so drop it, then rerun regression. After, we realize lag3 is not significant, so rerun, then second lag ends up not being significant, rerun with dropping it.
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X)-measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model Yi=β0+β1Xi+εi. The results of the simple linear regression are provided below. Y=−2,700+20X, SYX=65, two-tail p value=0.034 (for testing β1) Interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model. A. About 95% of the observed service charges equal their corresponding predicted values. B. For every $1 million increase in sales revenue, we expect a service charge to increase $65. C. About 95% of the observed service charges fall within $65 of the least squares line. D. About 95% of the observed service charges fall within $130 of the least squares line.
D. About 95% of the observed service charges fall within $130 of the least squares line.
Decision criteria that are used for decision-making when probabilities are unknown include: A. Maximin B. Maximax C. Minimax regret D. All of the above E. None of the above
D. All of the above
In selecting an appropriate forecasting model, which of these approaches are suggested? A. Measure the size of the forecasting error. B. Use the principle of parsimony. C. Perform a residual analysis. D. All of the above
D. All of the above
What does the width of the prediction interval for the predicted value of Y dependent on? A. The standard error of the estimate B. The value of X for which the prediction is being made C. The sample size D. All of the above
D. All of the above
What model can be used to make predictions about long-term future values of a time series? A. quadratic trend B. linear trend C. exponential trend D. All of the above
D. All of the above
Which of the following statements is not true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C. A feasible solution point does not have to lie on the boundary of the feasible solution. D. An infeasible solution violates all constraints.
D. An infeasible solution violates all constraints.
Which of these statements is true regarding the coefficient of multiple determination r2Y1.2? A. It will have the same sign as b1. B. It measures the proportion of variation in Y that is explained by X1 holding X2 constant. C. It measures the variation around the predicted regression equation. D. It measures the proportion of variation in Y that is explained by X1 and X2.
D. It measures the proportion of variation in Y that is explained by X1 and X2.
What provides an upper limit for how much one should pay for additional information to improve our decision? A. expected monetary value (EMV) B. expected value under certainty (EVUC) C. expected value under risk (EVUR) D. expected value of perfect information (EVPI)
D. expected value of perfect information (EVPI)
What represents the upper limit of how much one should pay to gather a sample to acquire additional information about the alternatives? A. expected value without sample information B. expected value with sample information C. expected value of perfect information D. expected value of sample information
D. expected value of sample information
When is the Cp statistic used? A. if the variances of the error terms are all the same in a regression model B. to determine if there is an irregular component in a time series C. to determine if there is a problem of collinearity D. to choose the best model
D. to choose the best model
The overall upward or downward pattern of the data in an annual time series will be contained in the ________ component. A. cyclical B. irregular C. seasonal D. trend
D. trend
The accompanying table is the list of MAD statistics for each of the models you have estimated from time-series data. Based on the MAD criterion, what is the most appropriate model? Model MAD Linear Trend 1.38 Quadratic Trend 1.22 Exponential Trend 1.39 Second-order Autoregressive 0.71 A. linear trend B. quadratic trend C. exponential trend D. second-order autoregressive
D. second-order autoregressive
The following Residuals are from a linear trend model used to forecast sales. Compute the MAD.
In Minitab, use function: MEAN(ABS('Residuals'))
exponentially smoothed graph interpretation
We would consider model e, the exponentially smooth model with w=.25, to be the most accurate because it has the smallest MAPE (mean absolute percentage error) out of all three graphs with 67.03. While graph c has a lower MAD (mean absolute deviation), it is just decimal points away from the MAD of graph e (43.03 compared to 43.53, respectfully). Therefore, it's safe to say that graph e is the most accurate out of the three. analyzing the graph based on the data - The number of IPOs in the US market start out decreasing and then increase a lot. Then, the number decreases a little and then spirals downward. Then, these numbers rise again, and just before the end of the period, once again decline sharply. The number of IPOs in the US market is inconsistent as it is constantly switching between increasing and decreasing. There is no pattern for the number of IPOs, as the models appear to be random and without pattern. This is consistent with the high MAPE value present within the data-you usually try to look for less than 20.
The _____________________ regret criterion minimizes the maximum regret. (fill in the blank)
minimax