QMB 3250 EXAM 3 Modules(17-24)
Regression Method
"the average" would be the average result or a weighted average.
Classification Method
"the average" would be the mode of the most frequent classification.
Two Way ANOVA P-values
*p-value < alpha = reject Ho (interaction is significant) *p-values > alpha = FTR Ho (interaction is Not significant, you can look at main effects instead).
OLAP (Online Analytical Processing) Machine Learning
- Asks specific question from a sample of data in hand. - Does not build predictive models. - Cannot be used to predict into the future. Ex. what percent of male college students between the age of 18-24 have more than $500 showed on a credit card?
Predictive Models (Machine Learning)
- Can be used to predict into the future based in data on hand. - It can have Regression or Classification problems.
Important things to know about data mining...
- I cannot solve un-asked questions. - it cannot fix incorrect data or bad data collection methods. - he cannot automatically find beneficial patterns for business. - it is still necessary to understand the business. - it is still necessary to have good data analysis skills. - the machines aren't really "learning".
Supervised Models (Machine Learning)
- Response variable is KNOWN. Can have regression and classification problems. Ex. study how much customers will spend online and predict into future.
Insupervised Models (Machine Learning)
- Response variable is UNKNOWN. - Cluster analysis Ex. group customers by buying habits.
Types of Algorithms
- Tree Models - Neural Networks
Autoregressive Models:
- allows for a seasonal component to be better modeled. - forecasts can be made for a few measures. - also sensitive to spikes.
Neural Networks (algorithms)
- an automatic, flexible, non-linear regression model. - it's methods are more like the smoothing methods of Time series than multiple regression. - it retains all the predictors although it may limit the effects of some. - model is not interpretable ➡️ black box model
Assumptions and Conditions for ANOVA
-Independence Assumption (Randomization Condition) -Equal Variance Assumption (Similar Variance Condition) -Normal Population Assumption (Nearly Normal Condition)
Kruskall-Wallace Test Assumptions
-Independence assumption -randomization condition -independent groups
Data Mining Process (CRISP-DM Cross Industry Standard Process for Data Mining)
1 - Business Understanding 2 - Data Understanding 3 - Modeling 4 - Evaluation 5 - Deployment or back to Business Understanding
Multiple Regression Based Models advantages...
1. Better at fitting series that have trend, cyclical, and seasonal components 2. Allow us to predict more than just the next point 3. Allow us to investigate each of the components separately
The types of experimental designs:
1. Completely Randomized Design 2. Randomized Block Design 3. Factorial Design
Types of weighted moving averages
1. simple exponential smoothing 2. auto regressive moving averages
There are two different types of modeling Time series...
1. smoothing methods 2. regression methods
How to use a Wilcoxon Rank-Sum/Mann Whitney Test to compare
1. use the Mean and Variance equations. 2. find the standard deviation (standard deviation will always be square root of variance and vice versa). 3. Find the Z-score
Weighted Moving Averages
A more sophisticated type of moving averages gives different weights to the values being averaged. Values that are further away get less weight.
Multiple Comparisons
A series of tests/intervals to determine which of the means are different. These tests take into account the fact that more than one test/interval is being conducted and controls for Type I error for all of them.
What do we need in order for our F Test Statistic to show evidence for the alternative hypothesis (Ha)?
A small P-value A larger F Test Statistic than our F* critical value.
Factorial Design
An experiment with more than one factor. Number of treatments are found by multiplying the number of levels for each factor. There can be interaction. A Full Factorial Design has observations at each treatment.
Expected Value with Perfect Information (EVwPI)
Can be found if we know the State of Nature and could pick the most cost-effective measure for that Nature.
Sums of Squares Error
Estimates how much variation there is within each group.
For a time series for simple exponential smoothing, a larger alpha is smoother than a shorter period.
False
Seasonal Component (time series)
Fluctuation occurs at roughly the same time each year (or day of the week or part of the month).
Seasonal components
Fluctuation occurs that roughly the same time each year (or day of the week or part of the month).
What type of test can we use? To determine the monotonicity of fertility rate and export/import revenues for 26 countries in Asia.
Kendall's Tau (Is used to measure monotonicity)
What type of test can we use? Determining if there is a difference in the grades for two customer service lines during the Thanksgiving Black Friday sales. There were 30 customers randomly selected at center A and 35 at Center B.
Mann Whitney Test (two groups with different sample sizes).
What type of model is best to use when there is a consistent percentage increase in the data?
Multiple regression-based model
When using Auto regressive models should we be concerned about the assumption of independence?
No, since we aren't performing tests on slope coefficients.
The time between two peaks is called...
Period
Test Statistic
Ratio at the variation of the beans to the variation of the individuals.
Two Way ANOVA Note
SST = SSA + SSB + SSI (interaction) + SSE
Wilcoxon Signed Rank Test critical values
TS < critical value = reject Ho = we have statistical evidence. TS > critical value = FTR = no statistical evidence.
For a Time series for simple exponential smoothing, a shorter alpha is smoother than a larger alpha.
True
For a time series for simple moving average, a larger period will be smoother than a shorter period.
True
In One Way ANOVA always makes sure that your X variable is categorical in JMP, and your Y variable quantitative.
True
In simple exponential smoothing, an alpha value of 0.2 is considered smoother than an alpha with a value of 0.5?
True
It is easier to compare between the group means if the within group variation is small. look at box plots.
True
It is harder to compare between the group means if the within variation is larger.
True
The sum of ranks (for samples larger than 10) has a nearly normal distribution?
True
R^2 should be close to 1 for it to be considered a good model. (T or F)
True - if you are retesting the R^2 needs to increase not decrease.
When looking at the w2 table, you must only use the n's that had a difference. If there was no difference you can ignore and subtract them from the total n value.
True - only the n with differences are used. ignore the zero's.
Comparative, double blinded experiment where placebos are compared with treatments or very valuable?
True - randomizing the treatments improves this comparison to make it the best type of experiment.
Interaction is when the effect of one factor depends on the level of the other factor.
True for interaction
Two Way ANOVA
Two factors with multiple levels. *by including information about levels of both factors more of the variation can be explained. we often look at the effects of the results using an interaction plot.
What rank sum do you use for the Wilcoxon Rank-Sum Test/Mann Whitney Test?
We use the rank sum from the smaller sample as the test statistics (if the samples are different sizes).
An interaction in Two Way ANOVA is...
When the effects of one factor are not similar across all levels of the other factor.
Block (in an experiment)
When we group subjects together. The factor that contains the groups is a blocking factor, and it's levels are called blocks. We can reduce the variation and even test for the affects for these groups. We use it when we believe a factor may affect the response variable and we want to control or account for it's affects. Can't assign them at random.
Kruskall-Wallace Test Statistic
Where Ti is the rank sum for each group and N is a total number of values.
The et in the Random Walks formula is sometimes described as...
White noise. They are random variables, independent and come from some distribution.
What type of test can we use? comparing the ratings of a new course between underclassland and upperclassmen. There were 10 upperclassmen and 10 underclassmen.
Wilcoxon Rank-Sum Test (two groups with same sample sizes)
Two Way ANOVA Table
a = # of Factor a levels b = # of Factor b levels r = # in each treatment
Big Data
a broad term for datasets so large or complex that traditional data processing applications are inadequate. There are 4 part's Volume, Variety, Velocity, and Veracity.
Give an example of why we might want to know the model.
a model that determines why an incarcerated person should be released on good behavior.
Non-Monotone (Kendall's Tau) relationship
about half of the pairs have a positive slope and half are negative slopes.
In Two Way ANOVA, we now test for...
affects the Factor A, Factor B, as well as interaction between Factors A and B. The anova table changes to address this.
State of Nature
are artifacts of the real world that will affect the results of these actions.
What other method does Random Forest start out the same as?
bagging
We don't want to use the t-test or t interval methods because...
because of the potential buildup of type 1 error.
After you determine that I factor significant, you can...
calculated confidence interval to compare means. *If you make more than one comparison, make sure that you control the type 1 error rate.
A Decision Tree...
can also demonstrates the decision-making process.
In what way is Random Forest similar to Bagged Trees?
each tree is made by sampling with replacement.
Negative Monotone (Kendall's Tau) relationship
for each pair of points, the slope between every pair of points is negative (single stream)
Veracity (Big Data)
potentially less quality in the data. Veracity refers to the accuracy data. Big data sets may have inaccuracies and lapses in data quality.
What method is used in neural networks to transform the data?
propagation - transforming the data into an s-shaped curve.
Ranks
responses that are NOT quantitative (ex. food ratings, satisfaction ratings)
MAPE summarizes the forecast error so the...
smaller it is, the better it is.
Longer periods in simple moving average ofwill have moving averages that respond more slowly, so longer periods are...
smoother
A table...
summarizes the outcomes in an organized way.
Outcomes of the decision process can be given in a ______________ or a __________________.
table or decision tree
A study...
the "experimenter" does not manipulate the treatments.
In One Way ANOVA, when the null hypothesis (Ho) is true...
the MSTR equals the MSE.
Outcomes or Payoffs
the consequences of the actions.
Velocity ( Big Data)
the data comes in swiftly and needs to be analyzed quickly.
In observational data...
the data is likely not randomly put into different groups or doesn't have treatments randomly applied; therefore, you can't show cost.
An experiment...
the experimenter manipulates the treatments.
Wilcoxon Rank-Sum Test/Mann Whitney Test (nonparametric test) MAIN IDEA: Neirher group is better...
the rankings alternate back and forth between the two groups.
Back Propagation
transforms the data into s-shaped curves.
Randomize (in an experiment)
treatments should be randomly assigned to the participants. To allow us to make sure that the affects beyond our control are spread out evenly across observational units.
All Multiple Comparisons Methods require the null hypothesis for the F test is rejected.
true - the Ho must be rejected.
Simple Exponential Smoothing
values that are closest to the estimated value get the most weight in the moving average and values that are further away get less. * doesn't usually work well when seasonal components are present.s
Actions
when a business has a decision to make and there are several choices.
What is the correct definition of a Random Forest?
when we construct a multitude of decision trees at training time and output the class that is the mode of the classes or mean prediction of the individual trees. every time a split is made only 10% of the predictors are considered.
What is the correct definition of bagging?
when we fit a model with training data, then fit a sample with replacement and fit another tree, and repeat the process many times.
What is a correct definition of boosting?
when we fit a small tree model with limited splits, reweigh the data depending on how it is classified, fit a new tree, and repeat.
2. bonferroni number of comparisons formula
where a = # of levels.
Alpha for Weighted Exponential Smoothing
- Alpha is close to 0.5, the most recent value and historic values are weighed the same . - Alpha is close to 1, the most recent value is given more weight. this is used if you want the series to react more quickly to irregular components. - Alpha is close to 0, the most recent value is given less weight than historic valleys. you want to use this if you want the series to react more slowly, creating a more stable series.
Advantages of Spearman's Rho and Kendall's Tau
- both can be used with ranks - both are not affected by outliers - not affected by re-expressing data
Simple Moving Average ( SMA):
- can be applied to almost anytime series. - can only forecast one period out. - sensitive to spikes. - has a hard time keeping up with a strong trend.
What steps could be taken to check the nearly normal condition in ONE WAY ANOVA tests.
- check the box plots in each group (level). - check the histogram of each group (level).
What is the idea behind neural networks?
- creating new functions from predictors (nodes) - collection of these notes create the hidden layer. - fitting is done by back propagation by transforming them into and s-shaped curve. - response
Wilcoxon Signed Rank Test Assumptions:
- data is paired (two observations from each case (individual). - differences are independent
Autoregressive Models can...
- do a better job at modeling quarterly trends. -It uses regression methods to determine the weights for previous terms. -The model is that an average of previous terms in the series with weights determined by regression.
Boosting
- fit a tree model - give higher weights to the items that are misclassified - make another tree - average or predict most frequent class
Bagging
- fit a tree model with training data - take a sample with replacement (bootstrapping) - fit another tree - average for predict most frequent class
Exponential Smoothing:
- gives you the control to wait the most recent or historic values differently from series to series. - can only forecast one period out. - sensitive to spikes. - has a hard time keeping up with a strong trend.
MAPE - Mean Absolute Percentage Error
- looks at the amount of error proportional to the original value - advantages (doesn't depend on the units, it is a percentage, so doesn't change the scale of y it's changed) * most common.
Regression methods
- model the behavior of the trend and cycle using methods that we learned in regression. - the advantage is that they can be used to predict further into time, although we should still be cautious about extrapolating too far from the data.
Disadvantages of Spearman's Rho and Kendall's Ta
- more advanced techniques/tests are not based on them
What is the difference between Data Mining and Statistics?
- much more data - more investigative, looking for patterns, but not conducting tests or estimating parameters. - data not collected through a defined collection method. *Data is often combined with data warehouse information. - the results allow for a business to describe on a certain course. *must be actionable. - The modeling is done automatically.
Expected Value (EV)
- probabilities must be legitimate. They should add up to 1. - you must multiply the probability and the outcomes. Then, you add all of the variables in the Action to find the Expected Value (EV) of that Action.
Which methods are best when you are dealing with seasonal data?
- regression-based models - Auto regressive models
Smoothing methods
- smooth out a regularities.. - there are no assumptions that must be made about the trend or seasonal component. - a disadvantage is that predictions are limited - they can only predict in the very short term. - these are usually only used for one period beyond the data recorded.
Irregular component
- sometimes there's variation that is not explained. - just like residuals, you should look at these values for anything unusual.
Tree Models (algorithms)
- sorts through predictor variables repeatedly to divide the data into groups to best determine the response variable. - it will continue to Branch until the number remaining in the sample is too small or there are no longer any big differences in the response variable. this and node is called the terminal node. - it handles outliers well. - it handles many potential predictor variables easily - cross-fitting is used to validate the model selections
MSE - Mean Squared Error
- sums the squares of the errors - disadvantages (large deviations, not the same units in the data, it's value is changed if the scale of y is changed.
MAD - Mean Absolute Deviations
- takes me absolute value of the errors. - advantages (doesn't have as large of a penalty for one irregular event, it is in the same units of the data) - disadvantage ( it's value is changed if the scale of y is changed) * this is called MAE in JMP.
Random Walk:
- the best prediction that we have of the next value is the current one. - there appears to be no other structure to the data.
Simple Moving Average
- this method creates a new time series from the original data by averaging adjacent values. - the number of values that are averaged is called the length (L). - the purpose is that it helps illuminate how the data is varying over time.
Data Mining Algorithms
- training sets-used to fix the model - test sets-used to determine if the model is valid. - A more involved process repeatedly divides the data set into training and test sets many times and cross validates multiple times. in this case the training set is 90% of the data, and the test set (now called the hold out set) is about 10% of the data. - to determine if it's a good model for Regression Models --- standard deviation of the residuals on the test set. --- R^2 = 1 - SSE/SST (can be negative) on the set. - to determine if it's a good model for Classification Models --- count up all the misclassifications.
Regression Based Models:
- use regression to model the trend in seasonal components. - extra variables (exogenous) can be added to help with modeling. - they can be used to forecast into the future, but caution should still be observed to not extrapolate. - you must decide if you are going to fit a multiplicative or additive model. - sensitive to outliers. - seasonal components must be similar in magnitude throughout the observed time.
Classification Problems for Predictive Models (Machine Learning)
- with a categorical response. Ex. based on behaviors of past customers, will the new company default on the proposed loan?
Regression Problems for Predictive Models (Machine Learning)
- with a quantitative response. Ex. based on past spending, what is the typical amount of spending on a credit card for adults 18-24?
Wilcoxon Rank-Sum/Mann Whitney Test Assumptions
-Independence assumption- randomization condition -independent groups
Disadvantages of simple moving average
-The moving average values can be affected by outliers (sharp peaks or falls). - Doesn't work well when there are strong seasonal, trend or cyclical components.
Wilcoxon Rank-Sum Test/Mann Whitney Test (nonparametric test)
-Wilcoxon = 2 groups w/same sample sizes -Mann Whitney = 2 groups w/different sample sizes -we don't have a parameter to specify in hypothesis statements. -we don't have to have quantitative data. -less powerful than a parametric test. -it's 95% as powerful as a two-sample t-test if we have data that can be used for both nonparametric and parametric. -distribution-free (no need to know the sampling distribution of a statistic).
Kruskall-Wallace Test (nonparametric counterpart to one factor ANOVA)
-compare 3 or more groups -rank across all groups and assigned average ranks to ties *use Kruskall Wallace when we have small samples, with a skew and evidence of large outliers.
Four principles of experimental design
-control -randomize -replicate -block
Spearman's Rho...
-data is replaced by ranks and then the correlation found between the ranks. -it is not influenced by outliers or by bends in the data or by re-expressing data. -Spearman's Rho goes from -1 to 1
When to use nonparametric tests?
-when you have only ordered data -when you have quantitative data but assumptions about normality are not met (outlier SKU data or more than one mode); however, we should still explore the characteristics of modality and outliers. -when you don't have linearity (although we expressing the data may be a better idea). -less powerful than parametric techniques.
Types of smoothing methods
1. Simple Moving Average 2. Single Exponential Smoothing Average (SES)
Components of a Time Series
1. Trend 2. Seasonal 3. Long Term Cycles 4. Irregular Components
Bonferroni Method can be used to find several hand calculations...
1. bonferroni individual error rate formula 2. bonferroni number of comparisons formula 3. bonferroni confidence level formula
Methods for Neural Networks
1. create notes (also called features) that are linear combinations of the predictors period all of these nodes together are called The hidden layer. there are multiple ways to come up with these linear combinations, but a popular method is called back propagation. this transforms the data into s-shaped curves. 2. then the response variable is fit by the s-shaped curves. this gives the method of flexibility.
Wilcoxon Signed Rank Test Method:
1. find the difference between each pair of observations. 2. ignore any of the differences that are equal to 0. 3. rank the absolute values of the differences (don't look at +-, yet) 4. sum up the ranks of all the positive differences (T+) and all the negative differences (T-). 5. pick the smaller of these two. this will be called T. 6. consult table W2 to determine the critical values.
Issues in Experimental Design:
1. placebos - a pale treatment 2. placebo effect - acting a certain way because you are given a treatment, even if it's only a placebo. 3. single blind - participant doesn't know which treatment they are receiving. 4. double blind - participant and experimenter don't know which treatment they are receiving/giving.
How to conduct a Wilcoxon Rank-Sum/Mann Whitney Test
1. put all of the ranks in order from both groups. 2. assign new ranks to each of the ranks (if you have more than one of the same rank you must get the mean of those ranks). 3. sum the New ranks for each of the groups. (choose the smallest total)!
Friedman's Test for a Randomized Block Design Method
1. rank within each of the blocks 2. sum the ranks for each treatment (Ti)
There are two types of observational studies
1. retrospective study 2. prospective study
In which scenario would you consider a non-parametric test?
1. when we might want to replace numeric values with ranks if we are concerned about outliers. 2. when we don't have quantitative data, but rather could have survey responses such as "strongly agree", "agree", etc.
One Way ANOVA Test
A statistical test used to analyze data from an experimental design with two or more means.
Lurking Variables
A variable that has an effect on the response variable but is not measured as part of the study of interest.
Completely Randomized Design
At least one subject is randomly assigned to each of the treatments.
If we wish to better model quarterly trends use the...
Autoregression model
Sums of Squares Treatments (SSTR)
Estimates how much the means vary. This value gets bigger just by adding another group, so Mean Squared Treatments is preferred. Y bar i, is the sample mean for each group. Y double bar, is the "grand mean".
For a time series for simple moving average, a shorter period will be smoother than a larger period because shorter periods do not react as quickly.
False
What type of test can we use? To compare the ratings of three tax preparation software packages conducted by six CPAs.
Friedman's Rank Test (to compare more than two blocks)
Friedman's Test for a Randomized Block Design hypothesis
Ho: all the medians are equal (OR: all treatments are identical). Ha: not all the medians are equal (OR: not all treatments are identical).
One Way ANOVA Hypothesis
Ho: mu1 = mu2 = mu3...muK= no difference in treatments. Ha: At least one population mean is different for the rest.
Kruskall-Wallace Test hypothesis
Ho: the centers for all groups are the same Ha: at least one of the centers is different
Two Way ANOVA hypothesis
Ho: the effect is the same at all levels. Ha: there is at least one of the means change for the level.
Wilcoxon Signed Rank Test hypothesis:
Ho: the median difference is zero Ha: the median difference is not zero
Wilcoxon Rank-Sum/Mann Whitney Test hypothesis
Ho: the two samples come from the same distribution (centers are the same). Ha: one distribution is shifted in location higher or lower than the other (centers are different).
Give an example of why we might NOT need to know the model.
If we have a model for reading handwriting on envelopes, we don't care what the actual formula is as long as it works correctly.
Random walks...
If you run an autoregressive model and the slope coefficient is almost 1 and the y-intercept is close 0. yhat@t+1 = y@t * it's also called the naïve forecast*
The smoothed value for time period # (ex. time period 72)...
Is the predicted value for time period #+1 (ex. time period 73).
Kendall's Tau
Is used to measure monotonicity. W e use it when we are interested in the direction of a relationship, but don't really care if the direction is linear.
Why is random assignment important in experiments?
It allows us to say differences in the results is really due to the treatments.
What type of test can we use? Determining if the ratings of a new course had similar ratings (on a five-point Likert scale) between students who had taken one of three possible prerequisites courses.
Kruskall Wallace Test (3 or more GROUPS)
Confounding Variables
Means the effects about two variables can be separated. When confounding Variables are present, the individuals affects cannot be teased out. The impacts of the two variables flow together but this doesn't necessarily tell us that one impacts the other.
Replicate (in an experiment)
Need reasonable number of participants so we can estimate variation. *replicates - repeated observations for a treatment. *balanced - when there are the same number of replicates for each treatment.
If there is no direction in the time series trend, this is called...
Stationary to the mean.
How are LAGS created in the data table?
The data is shifted by one cell down each time you copy it to the right of the original data.
Randomized Block Design
The experiment contains blocks which cannot be randomly assigned. Treatments are the ones that can be randomly assigned within the blocks.
Randomized, Comperative Experiments...
The experimenter applies treatments or manipulates the variables and observes the results. Treatments are assigned at random. The result is a response variable (y), which may be a categorical or quantitative variable.
Modeling a trend that is linear (Multiple Regression Based Models) consistent increase or decrease...
This is considered an additive. The slope can be interpreted as it wasn't simple linear regression.
Modeling a trend that is exponential (Multiple Regression Based Models) - meaning a curve on the scatter plot...
This is considered multiplicative. You have to take the log (time series). The slope has to be reexpresses with Log^slope in order to have an accurate interpretation of the slope. *this will usually yield a better model.
What type of test can we use? Modeling the revenue for IBM computers for the past 15 years?
Time Series (data measured at regular time intervals).
Match each non-parametric test with its correct definition? Friedman
To compare the ratings of three restaurants by 7 food critics.
Match each non-parametric test with its correct definition? Wilcoxon Signed Rank Test.
To determine if the ratings of a new plagiarism software are better than TurnItIn. Each software was rated by 10.
Match each non-parametric test with its correct definition? Kendall's Tau
To determine the monotonicity of GPA and socioeconomic status in 50 cities in the US.
Match each non-parametric test with its correct definition? Spearman's Rho
To measure the association between two variables.
What are the key differences between trends and seasonal components in time series data?
Trends are a consistent pattern (either linear or curves) that approach either a negative or positive direction; Seasonal Components are fluctuations in data that occur around the same time every period.
What type of test can we use? Determining if the ratings of a new tax preparation software program were better than TurboTax. Each program was rated by 10 people.
Wilcoxon Signed Rank Test (two observations from the same pair of individuals - paired data)
Wilcoxon Signed Rank Test
a non-parametric test that looks for differences (median/centers) between two related samples. *It's the nonparametric equivalent of the matched pairs t-test. *there needs to be two observations from the same side of individuals*
Machine Learning
computer algorithms based on regression ideas. They are more automatic and flexible than methods we have learned so far. (OLAP, Predictive Models, Supervised Models, and Unsupervised Models).
Tukey's Method
controls the family wise error rate at a set level, by adjusting the confidence levels of all of the individual confidence intervals.
Boosted Trees
creates many trees - ensemble each tree is made by sampling with replacement.
Observational studies is where ...
data is not collected in an organized or controlled experiment.
Volume (Big Data)
data that you can't use conventional methods to investigate. to large!
A model handles outliers well, handles many potential predictor variables easily, and sorts through predictor variables repeatedly to divide the data into groups to best determine the response variable.
decision tree
Variety (Big Data)
different types of data. (ex. categorical, text, images, links.)
What is the appropriate next step if there is significant interaction?
do not look at the main effects, but look at multiple comparisons for each of the levels of each factor.
Control (in an experiment)
experimenter makes sure that experimental conditions are the same for each participant (controlled), and there needs to be a group that receives the standard or no treatment, this treatment is called control group.
How to find the Expected Value with Perfect Information (EVwPI)
find the most optimal action and calculate the expected value with a probabilities of that State of Nature. Then, find the absolute value of the difference between the expected value of perfect information and the optimal strategy. this is called the expected value of perfect information ( EVPI).
Random Forests
fit a tree model with training data, take a sample with replacement, fit another tree, average are predictable frequent class. but every time a split is made only about 10% of the predictors are considered.
Positive Monotone (Kendall's Tau) relationship
for each pair of points, the slope between every pair of points is positive (single stream).
In boosting, does misclassified data get a higher weight or a lower weight?
higher weight
Under the null hypothesis of no differences, what would the Rank Sum be close to?
if there's no difference, we would expect the rank sum to be close to the halfway point between 1 and n(n+1)/2.
Maximax Choice
if you were talking about returns -- maximum return.
If a modeling method is described as a black box, what does this indicate?
in a black box model, the equation that evolves is not interpretable.
What is the difference between multiple regression and neural networks?
in multiple regression we have a linear relationship but in neural network we don't.
Modeling seasonal components by using...
indicator variables. *remember that the indicator variable estimates the difference (positive or negative) of that season from the base season; therefore it may go up or down.*
What is the correct definition of interaction?
interaction is when the effects of one factor are not similar across all levels of the other factor.
In the F test statistic, what does the denominator measure?
it measures the variance within the groups.
In the F test statistic, what does the numerator MSTr measure?
it measures the variation between the treatments.
Friedman's Test for a Randomized Block Design Test Statistic
k= # of treatments (groups) b= # of blocks (# of raters) *You can find a p-value from the chi-square test with k-1 df, where k is the number of treatments*
An Auto regressive model uses ________________ variables, and is also better at modeling ____________________ trends.
lagged variables; quarterly trends
Minimum Choice
look at the minimum costs and then chose the lowest cost of the actions.
Retrospective study
looks back into time and looks at behaviors that have already occurred. This might suggest a hypothesis for the future.
Prospective study
looks forward into time. A question is made, and then subjects are determined, and then data is collected into the future.
Minimax Choice
minimize the maximum cost. *look at the max costs and then chose the lowest cost of the actions.
A trend that continues in one direction in Kendall's Tau is called...
monotone
Kendall's Tau is used to measure?
monotonicity
A model is an automatic, flexible, non-linear regression model, not interpretable, and retains all predictor variables although it may limit the effects of some.
neural network
Do neural network models reduced the number of predictors?
no, all predictors are kept.
When examining for box plots, which characteristic would tell us that there was a violation of one of the assumptions for One Way ANOVA?
one of the plots had a range that was three times the other plots.
In a decision tree, a __________ node to notes a decision whereas a ____________ node denotes something that is driven by nature.
square; circle
If there is no direction on the trend (data), it is called...
stationary to the mean.
In One Way ANOVA, when the null hypothesis (Ho) is NOT true....
the MSTR is much larger than the MSE.
What does a LARGE F Test Statistic indicate?
the difference between the sample means is larger than within the group variation.
What does a SMALL F Test Statistic indicate?
the difference between the sample means is similar (about the same) to the within group variation.
What does it indicate to have interaction in Two Way ANOVA?
the effect of one factor is not similar across all levels of the other factor.
What does it indicate to say that neural networks are Black box model?
the equation that is developed in neural networks is not interpretable.
Lagged values: lag 1 is...
the last value in the table ( not the first time value)!
When looking at an interaction plot, how can we tell if interaction may be present?
the slopes of the two lines cross or may cross at some point.
If there was truly no difference in the Wilcoxon Signed Rank test method, what would we expect to see for these values?
the values of T+ and T- would be roughly the same.
Wilcoxon Rank-Sum Test/Mann Whitney Test (nonparametric test) MAIN IDEA: One group is clearly better...
then all of the support lines grades are higher than the others.
The ANOVA F test only tells us if...
there is evidence that the means are different, but it doesn't tell us which one is different.
Data collected overtime at regular intervals, we have a...
time series (daily, weekly, monthly, quarterly, yearly).
Friedman's Test for a Randomized Block Design
to compare more than two blocks.
Fluctuation for seasonal components is of the same magnitude and in the same direction?
true
Dunnet's Method works well...
when you have a control group, you may be interested in comparing each group only with that of the control.
1. bonferroni individual error rate formula
where alpha = family wise error rate where j = # of comparisons
3. bonferroni confidence level formula
where alpha = family wise error rate where j = # of comparisons
If interaction is NOT present in Two Way ANOVA...
you can estimate the main affects.
Finding a p-value for the Kruskall-Wallace Test
you can get a p-value from the Chi square distribution where df=k-1, with k being the number of groups.
If interaction IS present in Two Way ANOVA...
you cannot talk about an average effect for a factor period instead, you need to talk about a factor effect at a level of a factor. A common approach is then to conduct multiple comparisons with each of the treatments.
Long-term cycles
you may also see the business cycle if you have long enough period of data to see this trend