68 terms

Business analytics 2

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Descriptive analytics
uses data to understand past and present
Predictive analytics
analyzes past performance to forecast future outcomes
Prescriptive analytics
uses optimization techniques to design processes
Business analytics
s the use of data, statistical analysis, quantitative methods, and mathematical or computer-based models to help managers make better, fact-based decisions.
Inferential Statistics
Drawing conclusions about a large group of individuals based on information about a subset thereof
Hypothesis Testing
Examining the veracity of a claim about the population

e.g., New CFL bulbs last no longer than standard incandescents
Population
All the items or individuals about which you want to draw a conclusion (the "large group")
Parameter
A numerical measure that describes a characteristic of a population
Operational Definitions
Universally accepted meanings that are clear to all associated with an analysis
Discrete Variables
variables that must be a whole number or finite, number of people or outcome on a coin flip, can't have half
continuous variables
can be half or any number in between, time is actually continuous
probability mass function
the cumulative height of each bar represents the % of the total that bin represents. tells us the probability of getting a certain value. this is when discrete.
probability density function
same as above but is the area under the curve and is for continuous variables and not discrete.
both probability functions must
equal 1
properties of a normal distribution
bell shaped

symmetric

mean, median and mode all equal
normal distributions spread is determined by the
standard deviation o
the range of a normal distribution is theoretically
-infinity to infinity
why do we use samples?
less time consuming and less costly

more practical than analyzing the whole population

can be more accurate than relating everything in a population
As sample size increases,
sigma descreases and we become more confident in our decisions.
Type I Error
Rejecting a true null hypothesis

Probability of a Type I Error is:
The level of significance of the test
Set in advance by the researcher
Type 2 Error
Failing to reject a false null hypothesis

Probability of a Type II Error is:
Directly related to the power of the test (1-Prob. Type II Error = Power)
Generally not computable (requires that population mean be known)
A sampling distribution is
the distribution of all of the possible values of a sample statistic for a given size sample selected from a population
Hypothesis testing is
analyzing the difference between the observed results and what you would expect if the null hypothesis were true
the p value is the probability of a
type 1 error which is rejecting a true null hypothesis.
As Sample Size Increases
Probability of Type II Error Decreases
What is a scatterplot?
Graphical representation of the relationship between two variables
relationships needed to understand from scatterplot
Magnitude
Correlation
Linearity vs. Nonlinearity
Outliers
limitations of scatterplot
Cannot infer causality

Limited to three covariates (at most), can be very difficult to analyze

Sub-population effects can be masked
Magnitude (Direction)
Magnitude is the overall trend in the data points

Positive?
Negative?
Zero (horizontal)?

Can be measured easily in Excel by adding a trend line to the plot
Correlation (strength)
Correlation is how closely related the values of X and Y are
Closely related values will produce points that are closer to a line
Less closely related values will produce a more dispersed cloud of points

Measured by the correlation coefficient
Linearity vs. Nonlinearity
Linear relationships produce points clustered around a straight line

Nonlinear relationships produce points that follow a curved line

We can't use linear methods to quantify nonlinear relationships
Incorrect conclusions
Invalid predictions
Costly consequent actions
you should delete an outlier if..
the data point is not relevant to the topic of study

the underlying data is flawed

You would want to keep it if the data is actually reflective of the real world
influential points
have a effect on or impact on the resulting analysis and conclusions.
residuals
difference between observed and predicted values
LOBF is determined by
the minimum of the sum of the squared residuals.
R squared
is the percent of variation explained by the dependent variable(s), relative to the overall variation in the data.

, R2 is how much more accurately we can estimate the outcome variable with the dependent variable(s) as opposed to simply using the average of the outcome variables
standard error only helps you when calculating the p value
...
statistical significance does not mean practical significance
...
adjusted r squared penalizes for each additional variable added to the data set.. It also doesn't carry the % of the variation explained aspect that r squared carries.
...
A model nests another when
it is a generalized version of it

Includes additional parameters
Does not exclude any parameters
Interaction Terms
Allows the effect of one variable on _𝑌_ to depend on the value of another variable
L.I.N.E Assumptions, what are these assumptions on
Have mean zero (Linearity) ,are probabilistically independent (Independence), Normally distributed, Equal Variance.

for all values of x the population errors
Linearity test
sample residuals must be in a linear line, residual plots
independent population errors
autocorrelation test, knowing the value of the errors for any set of x values provides no information on others
normally distributed test
plot the residuals on a histogram or qq plot , should be roughly bell shaped

Can also use a normal probability plot but it will be harder to analyze compared to the histogram of the residuals.
equal variance test
can be seen by plotting y on x OR RESIDUAL PLOTS

fan shape = heterskedastic

consistent = homoskedastic
Multicollinearity
Occurs when one variable is a linear combination of one or more other variables

No new information available on which to estimate parameters
Transformations
Transformations are simply the original variables altered by some mathematical function

two earlier transformations were scaling and interaction terms
WHEN YOU USE THESE TRANSFORMATIONS YOU CANT USE R SQUARED ANYMORE OR ADJUSTED OR STANDARD ERRORS
elasticity interpretation
when you log both the variable and the y hat you get the percentage change in estimate due to percentage change in variable which is determining elasticity
Stepwise Regression
Any process that automates the include/exclude decision rules based on some measure of fit, e.g.,
Adjusted R2
Parameter p-values


types = forward, backward, stepwise
tradeoffs in step wise regression
positives: may help identify important variables
can help sift through a large amount of variables

negatives:
can capitalize on sample randomness
won't account for transforms or interactions
very bad for understanding relationships but good for predicting
you could find a model that works perfectly with your sample but will be useless to use in the future.
three types of forecasting approaches
Judgmental - Qualitative
Extrapolation - Time Series
Econometric - Regression
Goal of forecasting is to make predictions
Accurately
Out of sample
Early
statistical and practical significance
does not imply causality

could be a third part variable causing this or

simultaneity: order events does not guarantee causality
combined forecasts
forecast errors might cancel out when combined across multiple forecasts: example= political polls
combining forecasts should increase confidence if...
the errors are random and independent across the polls
trend
the overall direction of the data
seasonality
short term repetitive patterns
cycles
long term shifts and patterns not as predictive

time between can change dramatically and may only be one or two within a data set
noise
random deviations from the pattern due to given observations
3 common examples of trend
linear
exponential
s-shaped
how to account for cycles in regression?
you must find a leading indicator and implement it within your data
autocorrelation can be helpful in identifying
seasonality

Positive: Large and small values tend to be followed by the same

Negative: Large and small values tend to be followed by the opposite
a larger span on a moving average will result in a
less impactful extreme observations
the average predicted college GPA, the average observed GPA and the predicted gpa of the average in the variables will equal each other.
...
core correlation
a variable is correlated with past values of other variables
autocorrelation
a variable is correlated with past values of itself.
when graph says something vs something else where is each variable placed
y vs x, so something on y axis
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