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quantitative business

Helena Back Englisch 27 Karten

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  1. 1Sampling distributionis a statistic that is arrived out through repeated sampling from a larger population, how the distribution of sample means differ across samples, from the example: each sample will consist of a different selection of three workers and therefore wages, the value of the sample mean will differ across samples
  2. 2Difference t distribution vs z distributionT distribution compared to z distribution has ticker tails since it accounts for more randomness (use SE instead of SD)
  3. 3What measures the Standard Error- It is an estimate for the standard deviation of the sampling distribution of the sample mean
    - It measures the extent to which the sample mean will differ across different samples
    - A large standard error implies that different samples from the sample population can give widely different sample means
  4. 4Motivate why the Standard Error depends positively on s:- s is (our sample estimate for) the standard deviation of the variable at hand
    - if s is large, i.e. if there are big differences between the population members, it should be intuitively clear that you can draw samples which give you very different means.
    - Or turn it around: imagine that s = 0, e.g. all students choosing Q9_4 = 4. In that case, every sample from the student population will consist of students choosing a 4, and every sample will therefore have a sample mean of 4. Consequently, the standard deviation of the sampling distribution will be zero.
  5. 5Motivate why the Standard Error depends negatively on n:- In larger samples, every observation is averaged out over a larger number of respondents
    - This makes the sample mean less sensitive to atypically low or high observations.
    - Thus, across different samples, the sample means will tend to be closer together
  6. 6Sphericitysphericity is the condition that the variances of the differences between all combinations of related groups are equal
  7. 7difference Anova vs Anova repeated measures- Regular Oneway ANOVA addresses the question whether the mean of a single variable is the same between several (sub- )populations. E.g.: whether the mean of Q9_4 is the same between the three nationalities
    - Oneway repeated measures ANOVA examines whether the mean of several variables is the same in a single population. (same as independent sample t-test and paired sample t-test)
  8. 8Null hypothesis of Chi-Square of Independence- The two variables at hand are indeed independent of each other. This implies that the gender distribution is the same across nationalities
    - Example: the same share of males and females among the Dutch students, the Germans and the others. Equivalently: that the nationality distribution is the same across the two genders; i.e. the same share of Dutch, Germans and others among male and female students
  9. 9Idea behind Ratio- If the differences between the treatments (the three motives (as measured by SST) are relatively large relative to the error sum of squares (SSE), then we have convincing evidence against the null hypothesis.
  10. 10H0: Multiple ComparisonsThis part of the output is about “pairwise comparisons”. The null hypotheses mean that, in the population, a pair of two (out of three) nationality groups are the same
  11. 11LSD confidence intervalLSD (Individual confidence intervals): standard confidence intervals, we compare the two means in each pair in turn, ex: we are 95% confident that the true difference in average mileage between gas types 1 and 2 lies somewhere between -2.77 and -0.51
  12. 12Tukey intervalsSimultaneous confidence intervals (Turkey method) = how confident can we be that all there three pairwise differences are simultaneously contained in the reported intervals
    Ex: We are % confident that, simultaneously the true difference between 1 and 2 is within … and the true difference between …
     confidence intervals under the Tukey method are often wider than the LSD method
  13. 13Type 1 error C- We look at each of the three comparisons individually, each time using a test with a significance level of 1%, which means that for every test, there is a 1% probability of a Type 1 error (reject a true null hypothesis)
    - If the null at hand were true, there is a 1% chance to reject it accidentally
    - From a simultaneous perspective, the probability that we make at least one Type 1 error among those three comparisons is then obviously larger than 1%  in fact, probably in the order of 3%. To reduce this probability, we will have to be more careful in rejecting our null hypothesis: in other words, we have to reject them less easily, this will be achieved by having higher p values
  14. 14Explanation HA:The alternative hypothesis is that one of the distributions is shifted w.r.t. the other. Full points require an explanation of this shift. In case H0 holds, then the distributions are identical, then it is a 50-50 issue whether the population if the respondents’ rates Q12c above or below. However, if the distribution is shifted to the right of that of Q15c, this means that the chance that the respondent rates Q12c above Q15c is higher than 50%
  15. 15H0: beta 12 = beta 21 = 0H0: beta 12 = beta 21 (beta 11 not included), the effect of the ten constructs on entrepreneurial intentions are the same among IB and Economics students, there will be a generic difference between the two programs, as captured by the dummy coefficient beta11, which does not have to be 0, graphically the slope of the model are the same for both study programs, but there may be an intercept difference
  16. 16H0: beta11= 12 = beta 21 = 0, ex: there are no differences between IB and Economics students, their determinant can be described by the same model, both the slopes and the intercept of the model are the same for both study programs
  17. 17Different modes time series dataTrend: the broad up- or downward movement of a series over time, i.e. its long-run growth or decline; captured by the regressor t in eq. (1).
    Seasonal variation: periodic patterns that are repeated on a strictly regular basis; captured by the monthly dummies in eq. (1).
    Cycle: recurring up-and-down movements around trend levels, but without strict periodicity, cf. the business cycle; captured by autocorrelation in the error term, i.e. by the -term in eq. (2).
    Irregular fluctuations: erratic movements without any recognizable pattern, “left over”after the other three regularities have been accounted for; captured by the “shock”part of the error term in eq. (2).
  18. 18purposes of factor rotation- Goals is to end up with factors which have clear interpretation
    - Would like to associate each original variable more or less uniquely with a single factor
    - Dots representing the original variables would bunch up along the upper ends of the axes that correspond with the factors
  19. 19Factor analysis rule of thumbThe standard procedures imply that, first, motives with an absolute factor loading above 0.7 can be unambiguously classified into the corresponding factor. Second, motives with absolute factor loadings below 0.7 but above 0.4 can be allocated to the factor where they have the largest loading. Third, motives with absolute factor loadings all below 0.4 cannot be allocated.
  20. 20Communalities:Communalitites: sth like the R2, means that …% of our variation of variable Q10_3 is captured by our two factors:
  21. 21mean purposes of factor analysis1) To better understand the structure of a set of variables
    2) To help design a questionnaire, suitable to measure underlying constructs of interest
    3) To reduce a dataset to a manageable size by reducing the effective number of variables, while retaining the information contained in the original variables as much as possible
  22. 22On which principles does SPSS determine the linear combinations?The key thing is that these linear combinations are defined in such a way that their variance (“eigenvalue”) is maximized, so that they represent the largest possible fraction of the information that is contained in our dataset. The first factor (with the factor loadings reported in the first column of the “Component Matrix”) is defined precisely in this way. It has a variance of 3.165, i.e. almost 29% of all the variance.
    The second factor is again a linear combination of Q10_1 to Q10_11 with the largest possible variance, but subject to the restriction that it must be uncorrelated with (“orthogonal to”) the first factor. Logically, it has a lower variance than this first factor.
    Similarly, the third factor is the maximum-variance linear combination that is uncorrelated with both the
  23. 23assumptions statistical analysis1) 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) The number of critical activities is sufficiently large for the CLT Theorem, even if the individual durations are Beta distributed (And often very skewed), their sum is approximately normally distributed
    3) The activity durations are independent of each other
  24. 24utility excerciseComment on the outcome: Cooperation, i.e. coordinated instead of individual decision-making, leads to higher individual (and therefore joint) contributions and utility. This occurs because the problem contains an obvious positive externality: each investor’s utility depends on the other one’s contribution, but that other investor will not take this “spillover” into account when deciding about his/her individually optimal contribution. In a situation like this, there may be a case for regulation.
  25. 25utility exercise- In Nash the total contribution to the joint project is below the socially optimal level of 64, thus in the Nash equilibrium we have underinvestment
    - Consequently, the joint utility of 48 is strictly below the level of 64
  26. 26Why do the best responses slope upward in Bertrand and downward in Cournot?In Cournot: quantity is negatively related to the demand of the competitor
    In Bertrand: quantity is positively related to the demand of the competitior
  27. 27Efficient market hypothesisThe efficient market hypothesis (EMH) or theory states that share prices reflect all information. The EMH hypothesizes that stocks trade at their fair market value on exchanges.

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Karteikarten am quantitative business, erstellt von Helena Back am 07/06/2022.
Erstellt von
Helena Back
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