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Flashcards

Quantitative Business Stats

Lia Hofmann Quantitative Business 5 English 39 cards

Cards in this deck (39)

  1. 1statistical analysis: 3 assumptions1. We assume that the project completion time is always determined by the durations of the activities which are critical in the deterministic baseline scenario
    2. Number of critical activities is sufficiently larger for the CLT to take effect
  2. 2Factor analysis correlation rule-of-thumbno correlation should be above 0.9 which would imply collinearity
  3. 3statistical analysis duration processes: 3 assumptions1. Assume that the project completion time is always determined by the durations of the activities which are critical in the deterministic baseline scenario
    2. number of critical activities is sufficiently large for the CLT to take effect -> sum is normally distributed
    3. The activity durations are independent of each other
  4. 4Process duration: calculate mean of probability distributionThe mean of CT is calculated by adding the means of the activity durations along the critical path
  5. 5Process duration: calculate standard deviation of probability distributionThe standard deviation is calculated by adding up the variances of the critical path and taking the square root
  6. 6Process duration: Why does the simulation give a higher mean value of completion time?In a simulation, the project durations are random and there is a certain probability that anotherpath may become critical -> completion time tends to be longer then. Unlike statistical analysis, simulation takes this effect into account -> the probability of critical paths other than the given one is sufficiently large to have some effect on the mean completion time
  7. 7Differences of P(CT<= deadline) and P(CT = deadline)according to the simulation, the probability to complete the project within any specific number of days is systematically smaller than according to the statistical analysis. The probability to complete the project within any given amount in time is smaller now
  8. 8Process duration: Why is the expected loss with a simulation larger than under statistical analysis?according to the simulation analysis, the project tends to last longer than according to the statistical analysis -> longer delays imply higher expected loss
  9. 9Use the table alongside to estimate the probability that each of the paths distinguished at i) will actually be critical.Activity C has probability 0 to be critical, hence all paths that include C cannot be critical.
    Activity A is unique to path 2, concluding that the path must be critical with the same probability that activity A is critical -> 0.125.
  10. 10two purposes of non-parametric tests1. analyze quantitative variables which violate normality and constant variance assumption -> normal parametric procedures would become dodgy at best
    2. analyze ordinal variables (for which the standard parametric tools would be incorrect because of "upgrading"
  11. 11Why is Chi-Square Test Goodness-of-fit alos non-parametric?Test does not require quantitative variables, nominal is enough
    -no assumptions about population distributions of the variables
    -only assumption is sample size being big enough to ensure expected frequencies equal to 5 or more
  12. 12Friedman test Null hypothesis and AlternativeNull: the distribution of the variables Q12a, Q12b, Q12c in the population are identical
    Alternative: At least one of these distributions is "shifted" with respect to the other two -> If two distributions are identical, if we randomly draw a participant it's a 50/50 issue
    -> if null can get rejected, the three distributions are probably not the same
  13. 13Null of the sign testIn the population of the customers, the median score for ... equals... (let's say 4)
  14. 14Characteristics about the Sign gtestSPSS counts all observations equal to the hypothesized median of 4 as part of S-, as if they were below the hypothesized median
    -> makes no sense because we could as well count the observations to S+ which would result ina. different value for our statistic
  15. 15imagine we would try to correct this “bug” in the output above, along the lines discussed in Case W3. Motivate as carefully as you can what will happen to the reported p-value (currently 0.193 or 19.3%) as a result of this correction.First, look at Observed Prop.
    If the hypothesized median/ Null is correct, we would expect something close to a 50-50; the closer away we are from a 50-50, the more evidence against the Null -> look at resulting proportions when taking out the observations
  16. 16Central Limit Theoremstates that the distribution of a sample approxiamtes a normal distribution (bell curve) as the sample size becomes larger, assuming all samples are identical size and regardless of population's actual distribution slope
    -> must be at least 30 for theorem to have an effect
  17. 17Law of large numberssample variances get approximately equal to the variance of the population as the sample size gets larger
  18. 18Parametric toolsare meant for quantitative "dependent" variables
    -For those tools to be valid, the variables have to satisfy some form of the "normality" and "constant variance" assumptions
  19. 19Vickrey auctionmaximize payoff and welfare through bidding trthfully after own evaluation
    -> always a best response
    -> Pareto optimal
  20. 20Economic interpretation of level curve c=3For an utility level of 3 (c=3), we can illustrate on a graph the combinations of payoffs (mü) and risks (stdev) for which utility equals 3
    -> for a negative value of c, the volatility will outweight the expected payoff
    A risk averse investor would want to invest in an asset with too much volatility -> that is why it yields a negative utility
  21. 21Factor analysis sample size rule of thumbRule-of-thumb: at least 10 to 15 participants per variables to get a stable factor solution, min of 300 participants
    -> can look at the communities if they are reasonably high at least 300 respondents are sufficient
  22. 22Correlationmeasures the degree to which two variables move in relation to each other
    -> positive correlation: as one variable move up the other moves up (move in the same direction)
    -> negative: as one variable moves up the other one moves down (move in opposite directions)
  23. 23Kaiser's CriterionAccording to Kaiser's Criterion, we retain factors with a total variance above 1
  24. 24Are motives captured to an acceptable degree?is tested against the average which is calculated with the cumulative variance of the retained factors -> sum up extractions and divide by count of variables
  25. 25deviation from Kaiser's criterion (retaining additional factors)Look at Scree plot, when averaging out (when does the line become flat)begins and we set the cut right before
  26. 26Direct Oblimin rotationidk
  27. 27Component plot in rotated space: reverse scale issues?Divide Questions into difefrent factors
    -> reverse scale issues are detectable with a negative value in the pattern matrix
  28. 28Rotated factors and correlatioCorrelations of the variables that are in the same factor are significantly high, while the correlation between variables of different factors are low/ insignificant
  29. 29Orthogonal rotationAn orthogonal rotation can be used if the correlation of the two factors is very low
  30. 30Normal diagnostic tools: Kaiser's ruleThe more variables that load onta a particular component (have a high correlation with the component), the more important the factor is in summarizing the data
  31. 31Eigenvalueis an index that indicates how good a component is as a summary of the data
    -> Eigenvalue of 1 means that the factor contains the same amount of information as a single variable
  32. 32oblique rotation.a transformational system used in factor analysis when two or more factors (i.e., latent variables) are correlated. It is one of two types of factor rotation used to identify a simpler structure pattern or solution, the other being orthogonal rotation.
  33. 33Direct Oblimin rotation-> concerning the two retaining factors that raise doubts for colinearity -> very low correlation
  34. 34How are Component Plot and Component in Rotated Space are related to the to the numbers in Component Matrix and Pattern Matrix?In the component Plot, each dot represents one of the eight motive and the coordinates along the Component 1 and Component 2 axes are equal to the factor loadings that are reported in the Component Matrix table
  35. 35Purpose of RotationIdeally, we would like to associated each motive more or less uniquely with a single factor
    Visually: dots representing the motives would bunch up along the ends of the axes that correspond with the factors
    -> Idea: to rotate the axes in such a way, that the ideal picture is more closely approximated
  36. 36allocate the eight motives as explicitely as you can to the two rotated factors1. motives with absolute factor loading above 0.7 can be characterized into the corresponding factor
    2. motives with absolute factor loadings below 0.7 but abve 0.4 can be allocated to the factor here they have the largest loading
    3. motives with absolute factor loadings all below 0.4
    Factor loading shows relative importance of some collection of items; score
  37. 37Concept of sampling distributionof bar here?because different 3-person samples from our population will consist of a different selection of three workers and therefore wages, the value of the sample mean will differ across samples
  38. 38first-order autocorrelationmeans that the error of Model (2) is lineatly related to the previous error, either positively or negatively
  39. 39Why would autocorrelation be a problem?

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5 Quantitative Business Flashcards on Quantitative Business Stats, created by Lia Hofmann on 31/05/2022.
Created by
Lia Hofmann · May 2022
Updated
Jun 4, 2022
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