Data Analytics for Management (Subject) / Final Revision / All (Lesson)
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- Which of the following statements about the mean is not always correct? The median is a measure of the middle (centre) value in a distribution The mean is a measure of the balancing point value in a distribution
- Measures of Shape (1) Kurtosis Fatness of Distribution Empirical Rules do not hold When high kurtoses, more extreme observations =KURT() (2) Skewness Right Skewed = Positive Skewness = Few stars have very large salaries, no players have really small salaries Left Skewed = Negative Skewness = Ratings
- The Three Empirical Rules: Interpretation of the Standard Deviation Approx. 68% are within 1 std from the mean Approx 95% are within 2 std from the mean Approx 99.7% are within 3 std. from the mean + measure in same unit as the variable + obeys empirical rules
- Measures of Variability (1) Variance Average of squared deviations from the mean (How far each point is away from the mean) Sums to 0 Found in Sample variance and unknown Population variance - squared units, i.e. squared dollars (does not always make sense) -> more natural: standard deviation (2) Standard deviation = Square Root of Variance (3) Range = Describes the amount of variablity in the data + Easy to compute, esp. if sample is small + Indicated how spread out data are - Very sensitive to outliers (4) IQR = Variability in set of data lessening the outliers, Third quartile minues the first quartile +Less sensitive than range , as Middle 50% range of data + Use For: Distributions that are skewed or have outliers (reported along with the median to represent the variabiliy and central tendency)
- Histogram & Cumulative Probability Distribution Histogram: Measures Count Values and their Probabilities Set of possible values and corresponding set of probabilities that sum to 1 Probability is height Cumulative Probability: A value is less than or equal to one The cumulative probability for X is 75%. This means that Probability (X ≤ 180cm)= 0.75 Equivalently, it means there is only 1-0.75 =0.25 or 25% probability that someone is taller than 180cm
- CAPM and Risk Systematic Risk = Market Risk - SSM Non-diversifiable Risk SP500 Unsystematic Risk = Diversifiable Risk - SSR Ideosyncratic Risk Firm-Specific Risk Can be eliminated Assumed to be 0 in CAPM
- Assumptions for Sample Mean and Sampling Distribution Assumptions Sample Mean Sample mean has same average value as individual observations SE is related to std of individual observations For large sample, the sample mean follows a normal distribution, irrespective of the shape of the distritbution followed by individual observations Properties of Sampling Distribution: Unbiased estimate of population Mean E(X) = ∪ SE is large when distribution is spread out (can be reduced with n) For large sample, the sample mean follows a normal distribution, irrespective of the shape of the underlying distritbution
- Regression Algorithm - Ordinary Least Squares Assumptions Average error is 0, no bias (overestimates ,underestimates) Average squared error minimized standard error of the residual errors
- Estimation Errors Non-Sampling Error Can be improved with sample size n Due to non-truthful responses Non response Bias Measurement Error (Wording) Voluntary response Sampling Error ineliminatable result of basing inference on a random sample Decreases with sample size n ↑ SD decreases Chance for Type l and Type ll Error decreases (acceptance area narrows)
- Central Limit Theorem For any population Distribution with mean and sd, the sampling mean x is approx. normal and improves as n increases, provided that n is reasonable large.
- Normal Distribution Two parameter family Location µ Spread σ Infinite No of Normal Distribution Combinations Standardizing: to measure variables with different means on a single scale = Normsdist(x) = Normsinv(p)
- T-Distribution When σ is replaced by s, the sample is no longer normal Shape determined by dof (small = wide, large, resembles Normal) Spread - slightly more spread than Normal