DESC 656 - Midterm
What is the value of the residual for X = 5 and Y = -19 given regression equation Yr = -1 -3 * X?
-3 ; Yr = -1 -3 *5 = -16, residual = Y - Yr = -19 - (-16) = -3!
What is the value of the residual for X = 5 and Y = -20, given the regression equation Yr = -2 - 3 * X, ?
-3 Yr = -2 -3 *5 = -17, residual = Y - Yr = -20 - (-17) = -3!
What is the numerical range for the smoothing coefficient?
0 to 1;
What is the probability for a third event outcome for a chance node if the probabilities for the first two events are 0.4, 0.5, respectively?
0.1
What is the probability of exceeding one standard deviation from the mean in a normal distribution?
0.16
What is the weight for the most recent value in a four period weighted moving average model based on the sum of the digits?
0.4; The sum of the digits for four periods is ten (1+2+3+4 =10). Therefore, the weight for the most recent value is 0.40 (4/10).
What is the correlation coefficient for two variables with perfect positive correlation?
1
Categories of business analytics
1) Descriptive 2) Predictive 3) Prescriptive
The four basic regression assumptions
1. The relationship between the dependent variable and the independent variable is linear. 2. Residuals are independent. 3. The residuals are normally distributed. 4. The variance of the residuals for various values of the independent variable is constant.
How many payoff cells are involved in a problem with four decisions and three states of nature?
12
How many payoffs are associated with a decision problem with four alternatives and three states of nature?
12
What is the expected value if X1 = 2000, X2 = 1000, P1 = 0.3, P2 =0.7?
1300
How many different regression models are possible given four predictor variables?
15
What is the expected value of a chance node with the following three payoffs (100, 200, 300) and the corresponding three probabilities (0.2, 0.3, 0.5)?
230
How many dummy variables are required to describe four types of religion?
3
How many states of nature are associated with a decision problem with five alternatives and 20 payoffs?
4
Which one of the following has the most risk based on the given coefficient of variation?
4
What is the trend projection for the following equation Ft = 75 - 5 * T for T = 6?
45 ; Substituting the value six (6) for the variable T in the equation yields the following result: Ft = 75 - 5 * 6 = 45.
What is the estimated value for Y given a value of X = 5 for the regression equation Yr = 25 + 4*X ?
45 Substituting the value of 5 for X into the regression equation yields: Yr = 25 + 4*X = 25 + 4 * 5 = 45
What is the approximate confidence level that corresponds to a critical t value of 2?
95%
P - Value
A p-value is the probability of obtaining a test statistic (e.g., t statistic) at least as extreme as the one that was actually observe assuming that the null hypothesis is true.
What does an interval estimate provide?
A probability range
What does a slope of zero between two variables indicate?
A slope of zero indicates a correlation coefficient of zero which suggests no linear correlation.
When to use a small value
A small value, around 0.2 or less, should be used for the smoothing coefficient when the time series (e.g., demand) is exhibiting large fluctuations.
Empirical rule
According to the empirical rule 95% of the area under the normal curve is contained within + 2 standard deviations.
Which one of the following is a benefit of business Analytics?
All of the Others: Can combine disparate data streams to improve business results. Data and analysis available at all times in real time.Makes processes more strategic to the business.
Which one of the following is a basic forecasting ground rule?
All of the others:Use X values within the database range, Common Sense, Use only statistically significant variables
R-square
Another expression for the coefficient of determination. R-square is equal to the sum of the squares of the regression divided by the total sum of the squares. R-square = SSR / SST
Decision tree
Arranges decision alternatives and states of nature as prescribed by the problem situation
EMV
Average monetary outcome of a decision if it was repeated a large number of times
Which modelling approach is used to revise past probabilities?
Bayesian
Which one of the following best describes subjective probabilities?
Bayesian
Represents the population regression slope coefficient
Beta
Which one of the following best illustrates a constraint?
Budget
Which one is a factor that plays a role in determining whether a good or bad outcome occurs regardless of the quality of the decision?
Chance
What does sensitivity analysis consider?
Changes in model coefficients
Which one of the following measures the amount of variability in Y explained by the regression model?
Coefficient of determination
Which one of the following measures risk?
Coefficient of variation
Prescriptive
Combination of both descriptive and predictive analytics (e.g. investment portfolio design, and airline flight schedule development).
What do correlation coefficients near -1 suggest?
Correlation coefficients near -1 suggest a strong negative association
What is the processed called of evaluating all possible values of variable in a model?
Data mining
How does the difference between R-square and the adjusted R-square change as the sample size increases?
Decreases
What is the impact on forecast accuracy as the values of the predictor variables vary from their means?
Decreases
What is the ratio that is used to determine the slope of the regression line?
Delta Y to Delta X
Which Analytics modeling approach seeks to measure and explain situations?
Descriptive
How is the residual defined?
Difference between Y and Yr
What are forecasting errors?
Differences between actual and forecast value ; Forecasting errors are the differences between the actual and forecast values. These errors are used in determining the best forecasting model.
Which one best describes the time series process?
Discover historical data patterns and project them into the future. An important aspect of the time series analysis is the process of smoothing the data.
Which expression best describes the maximum worth of perfect information?
EPPI - EMV
Which of the following is a suggested approach to effectively implement solutions?
Engage everyone affected by the decision in all steps of the problem-solving process
Which one is NOT an objective of decision analysis?
Ensure good outcomes
Decision Analysis
Evaluates alternatives & help business leaders choose the best course of action
Payoff value
Exists for each pair of decision alternative and state of nature
What do the initials EPPI stand for?
Expected payoff with perfect information
Which one of the following decision criterion is used to determine the optimal strategy given a payoff matrix with associated probabilities?
Expected value
Which one of the following is a reason that using Analytics may result in a lack of ultimate success?
Failure to define the real problem
Which one of the following is NOT a benefit of mathematical modelling?
Finds the right answers to incorrect or flawed problem statements
Business Analytics
Focuses on identifying & Leveraging business opportunities.
What is another term for predictive analysis?
Forecasting
Which one of the following describes how a decision-maker views or perceives a problem?
Framing
Procedures for developing a multiple regression model
Full, Backward stepwise, and Forward stepwise. The full model includes all of the independent variables whether they are significant or not.
What is the relationship between the dependent and independent variables called?
Function
Which of the following best characterizes an independent variable?
Function value depends upon its value
Predictive
Generates forecast about the future
How are states of nature assigned probabilities?
Historical data, Judgemental, Interviews
What is the standard null hypothesis for testing the regression slope?
Ho: b1 = 0
Which of the following methods of selecting a strategy is consistent with risk averting behavior?
If two strategies have the same expected profit, select the one with the smaller standard deviation.
Which one is NOT a step in the decision analysis process?
Implement solutions
Which of the following is NOT a step in a typical Analytics assessment?
Implement the results
Which one of the following problem-solving steps is often considered the most difficult?
Implement the solution
Which variable is plotted on the horizontal axis in a scatter diagram?
Independent Variable
What does multicollinearity measure?
Independent variable correlation
Potential "problems" associated with multicollinearity?
Insignificant t-scores and significant F ratio, Reverse coefficient signs,Inflated standard errors
What are short-term, unanticipated, and nonrecurring factors in a time series?
Irregular events
What causes irregular events?
Irregular events result from short term fluctuations in the time series which are neither systematic nor predictable, e.g., natural disasters.
Which one is associated with the decision with the smallest EOL?
Largest EMV
What is the primary purpose of data smoothing?
Look for a trend ; The purpose of data smoothing is to make the presence of a trend clearer by reducing the effects of other fluctuations.
Which one of the following is NOT a standard forecasting error measurement?
MEM
Which decision rule optimistically assumes that nature will always be "on our side" regardless of the decision?
Maximax
Which decision rule is associated with the smallest maximum opportunity loss?
Minimax
Which principle is OLS based on?
Minimizing the sum of the errors squared
Why is sensitivity important?
Most model coefficients are estimates
Which forecasting method is based on the arithmetic mean?
Moving average; The moving average is a statistical technique that computes a mean based on a specified number of observations. The moving average is used to smooth out the fluctuations of a time series.
Which modelling approach is best when there are multiple decision criteria?
Multi-attribute analysis
Issues with Multicollinearity
Multicollinearity can result in the estimate of one variable's impact on y, while controlling for the others, to be less precise than if predictors were uncorrelated with one another. Additionally, some of the predictor variable coefficients may have reverse coefficient signs and some of t-scores may be low but the F score may be significant.
What does a slope of zero suggest regarding the linear relationship between two variables?
No linear correlation
Which category of decision rules contains the maximax decision criterion?
Non-probabilistic
Which expression characterizes the break-even model?
None of : Fixed Costs / (Unit revenue - Unit variable cost). (Fixed costs + Unit variable cost)/ Unit revenue. (Unit revenue - Unit variable cost)/ Fixed costs.
Which one of the following is not a basic regression model assumption?
None of the others; Linear relationship between X and Y, Residuals are normally distributed, Error terms are independent
Which one is NOT a decision rule for applications involving uncertainty?
None of: Minimax regret, Maximin, Maximax
Which one of the following is NOT a basic component of a time series?
Normal The four basic components of a time series are the trend, seasonal, cyclic and irregular.
What is the adjusted R-square based on?
Number of predictor variables and sample size
Which one for the following is NOT a standard multiple regression analysis procedure?
Partial pairwise
What is the sign of the slope when the correlation coefficient is positive?
Positive ; The sign of the correlation coefficient and the slope must be the same
Which of the following is NOT true regarding the the use of probabilities in a payoff table?
Probabilities are always obtained from historical data
What is the first step in the decision-making process?
Problem recognition and definition
Which is the dependent variable in the following expression: Profit = Revenue - Costs?
Profit
Which one of the following indicates the two broad decision categories?
Programmed and non-programmed
Adjusted Coefficient of Determination
Proportion of total variance in the dependent variable explained by the independent variables adjusted for the sample size and the number of predictor variables.
Descriptive
Provides insight into what has already happened
Which of the following is a benefit of Analytics in the decision-making process?
Providing a structural context, Quantifying outcomes, Incorporating uncertainty
What is another expression for the coefficient of determination?
R-square
What does R-square measure?
R-square measures the amount of variability in the dependent variable explained by the independent variable.
Which one of the following is NOT a component of the cyclical variation?
Random
Which one of the following is a characteristic of R-square?
Ranges between 0 and 1
What is the appropriate decision when the p-value is less than alpha?
Reject Ho
Coefficient of determination (R-square)
Reports the proportion of total variance in the dependent variable explained by the set of independent variables.
What is the difference between Y and Yr called?
Residual
Which one of the following is NOT an input to the Bayesian model?
Revised probabilities
Which one describes a decision maker whose marginal utility of money diminishes?
Risk averse
Which one describes a decision maker whose marginal utility of money increases?
Risk taker
Which one of the following statements regarding the slope is true?
Same sign as the correlation coefficient
What graphic is best for detecting a trend in a time series?
Scatter Diagram ; A scatter diagram is a graphic display of data plotted along two dimensions. In a time series analysis the X-axis is time. Scatter diagrams are useful for detecting potential relationships between two variables such as a trend.
Which of the following terms describes the overall long-term tendency of a time series?
Seasonal
Which component may be ignored if data for a time series analysis is collected only on an annual basis?
Seasonal; The seasonal component represents a pattern of change that is completed within one year and repeats itself regularly over the time series.
Which one of the following best characterizes the role of Analytics in the decision-making process.
Should produce better outcomes on a more frequent basis
What value should the smoothing coefficient take on to be responsive to large demand changes?
Small
What is the primary purpose of the moving average model?
Smoothing; The primary purpose of the moving average model is to smooth out the fluctuations in the time series in order to look for a trend.
Which one of the following would have the largest seasonal usage variation?
Snow blowing equipment; Typically, the demand for snow blowing equipment would be high during the winter months and near zero during the summer months.
Which one of the following describes the coefficient of variation?
Standard deviation / Expected value
Which one of the following influences the payoff of a decision based on probability assignments?
States of nature
What are the two basic structural components of a payoff matrix?
States of nature and alternatives
What is the standard procedure used to select only statistically significant variables for the regression model?
Stepwise
A correlation coefficient of - 0.8 suggests a?
Strong negative association
Which one best defines problem-solving or decision-making?
Taking some action or making changes to an existing policy or procedure
What does Ho:b1 = 0 suggest?
That is the slope is assumed to be equal to zero which suggests no linear relationship between the independent and dependent variables.
What does the coefficient of determination (COD) measure?
The coefficient of determination (COD) or R-square measures the amount of variability in Y explained by the regression model.
Range of correlation coefficient
The correlation coefficient ranges in value between -1 and +1. A coefficient of -0.2 suggests a weak negative correlation.
Where does a correlation coefficient range?
The correlation coefficient ranges in value from -1 to 1. A value near zero suggests no linear correlation. A value of 0.2 suggests a Weak positive association!
Residual/error term
The difference between the actual Y value and the Yr value generated by the regression model is called the residual or error term.
Four basic components of business cycle
The four basic components of business cycle are the upswing, contraction, the trough and the peak.
Which principle is used to fit the regression line?
The method of ordinary least squares is used which is based on the principle of minimizing the sum or the errors squared.
How many dummy variables are required to describe four types of religion?
The number of dummy variables required to describe a categorical variable is N -1 where N is the number of categories. A variable that measures four different religions would require three dummy variables (i.e., 4-1 = 3).
Adjusted coefficient of determination
The proportion of total variance in the dependent variable explained by the independent variables adjusted for the sample size and the number of predictor variables. As the sample size increases the difference between R-square and the adjusted R-square decreases.
What does the coefficient of determination measure?
The proportion of variation in Y explained by the predictor variables.
What is a slope?
The slope is the difference in Y divided by the difference in X or <mi mathvariant="normal">Δ</mi>Y to <mi mathvariant="normal">Δ</mi>X
What is the numerical range for the simple exponential smoothing model?
The smoothing coefficient for the simple exponential smoothing model ranges in value between zero (0) and one (1).
What does a seasonal trend represent?
The trend, if present, represents the overall long-term tendency of a time series which can be either upwards or downwards.
What are the three most used error measurements
Three of the most widely used error measurements in time series analysis are mean absolute deviation (MAD), mean squared error (MSE) and mean absolute deviation (MAPE).
Which one best describes the role of Analytics?
To help improve the decision-making process
What is the gradual shifting of a time series over a long horizon called?
Trend ; The trend represents the long-term direction of the time series. Trends can be detected using a scatter diagram particularly after the data has been smoothed.
What are the four basic components of a time series?
Trend, Seasonal, Cyclic and Irregular
True or False: The slope and correlation coefficient have the same sign.
True
Which one best describes states of nature?
Uncontrollable events such as floods or war
Which of the following are types of decision-making environments?
Under certainty, Under uncertainty, Under Risk
Stepwise procedure
Used for selecting predictor variables to enter (forward) the regression model or to be removed (backward) from the regression model.
Beta
Used to represent the population regression coefficients where β0 is the Y-intercept and β1 is the slope for the first predictor variable.
Bayesian analysis
Uses prior information
Which one of the following best describes decision tree probabilities?
Uses prior information
Which of the following is NOT a primary problem in the decision-making process?
Using Analytics to support the process
What does a correlation coefficient of -0.2 suggest?
Weak negative association
What does a correlation coefficient of 0.2 suggest?
Weak positive association
When does multicollinearity occur?
When two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates may change erratically in response to small changes in the model or the data.
Criteria
Which one represents factors that are important to the decision maker?
Where is the independent variable plotted on a scatter diagram?
X-axis
Where is the dependent variable plotted on a scatter diagram
Y-axis
Time series Analysis
a set of observations on a quantitative variable collected over time.
Extrapolation models
analyze past behavior to predict the future.
How is the accuracy of a forecast measured?
by the confidence interval, decreases as the values of the predictor variables used in the regression forecast varies from their mean values (both above and below).
Seasonal patterns
happen in both stationary and non stationary
nonstationary
have upward or downward trend in data over time.
Goal of Extrapolation model
identify function f() that produces accurate forecasts of future values of the time series variable.
Simulation
involves the analysis of a complex decision situation by performing a large number of iterations to determine the probability distribution
Stationary time series
no upward or downward trend in data over time.
Confidence interval
provides a range estimate for a population parameter (i.e., slope). always expressed in percentage terms. For example, a common confidence interval is 95%. The end points of the confidence interval are referred to as confidence limits.
What statistic is used to judge the statistical significance of the individual variables?
t
t - statistic
used to judge the statistical significance of each of the independent variables. The process involves comparing the critical t statistic with the computed t statistic based on the sample data. If the absolute value of the computed t statistic is greater than the critical t statistic then one can conclude that the slope is not zero.
Which Greek symbol represents the error term?
α