MSIS 3223 Exam 2 Content

Properties of Probability Density Functions:

-density function must lie at or above the x-axis. -total area under the density function above the x-axis is 1. -For continuous random variables, there are an infinite number of values. -Calculates the probability of a random variable lying within a certain interval. -P is the area under the density functions between a and b. must lie between specific intervals

The probability of the component of an event equals

1-P(A)

normal distribution- empirical rule

68% of the data is within 1 standard deviation, 95% of the data is within 2 standard deviations, and 99.7% of the data is within 3 standard deviations.

Which of the following is true of normal distributions?

The mean, median, and mode are all equal.

Normal distribution:

a continuous distribution described by the familiar bell shaped curve.

Multiple linear regression:

a liner regression model with more than one independent variable. the iv in the spreadsheet must be in contingious columns.

R-squared is

a measure of the "fit" of the line to the data and will have a value between 0 and 1. The larger the value of R-squared, the better the fit. called the coefficient of determination

Random variable:

a numerical description of the outcome of an experiment.

The Delphi Method:

a popular judgmental forecasting approach which uses a panel of experts, whose identifies are typically kept confidential from one another (promotes unbiased exchange of ideas)

Multiple regression:

a regression model that involves two or more independent variables.

Index

a single measure that weights multiple indicators, thus providing a measure of overall expectation. provides direction of change, not a complete forecast used in judgmental forecasting

Time series model:

a stream of historical data.

Regression analysis:

a tool for building mathematical and statistical models that characterize relationships between a dependent variable and one or more independent, or explanatory, variables, all of which are numerical.

Outlier:

an extreme value that is different from the rest of the data.

Binomial distribution:

can assume different shapes and amounts of skewness, depending on the parameters.

A probability density function:

characterizes outcomes of a continuous random variable.

p values

checks for significance of the iv in regression models the lower the p-value, the greater the statistical significance of the observed difference p values <=0.05 are statistically significant

Is age discrete or continuous variable?

continuous because age is an infinite number A person could be 22 or 22.35, 22.3569

Multiple R and R Square:

correlation coefficient and the coefficient of multiple determination respectively. They indicate the strength association between the dependent and independent variables.

Expected value (of a random variable):

corresponds to the notion of the mean or average for a sample. also known as the probability weighted average

Power functions:

define phenomena that increase at a specific rate. mathematical functions used in predictive analytical models which define phenomena that increase at a specific rate. y=ax^b

Cyclical effects

describe ups and downs over a much longer time frame, such as several years

Cyclical effects:

describes ups and downs over a much longer time frame, such as several years.

Continuous random variable:

has outcomes over one or more continuous interval or real numbers. The set of values comes from an infinite number EX: pressure, height, mass, time, weight, density, volume, temp, distance

Simple regression:

involves a single independent variable.

Standard Error:

The excel output is the variability of the observed Y-value from the predicted values.

Time series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect:

is one that repeats at fixed intervals of time, typically a year, month, week, or day.

Which of the following is true about variance?

it measures the uncertainty of a random variable.

Indicators are

measures that are believed to be influenced by behavior of a variable we wish to forecast.

Perhaps the most important distribution used in statistics:

normal distribution

Before launching a new line of toys, Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, Toys Inc.:

noted the consumer response to similar previous products to marketing campaigns and used the responses as a basis to predict how the new marketing campaign might fare.

Interaction:

occurs when the effect of one variable is dependent on another variable.

A seasonal effect is

one that repeats at fixed intervals of time, typically a year, month, week or day

Permutations

order does matter count the number of unique outcomes where the order matters EX: Selecting a 1 and then a 3 is different than selecting a 3 then a 1

Combinations

order doesn't matter Count the unique outcomes

A seasonal effect:

repeats at fixed intervals of time, typically a year, month, week, or day.

Linear functions

show steady increase or decrease over the range of x and is the simplest type of function used in predictive models. easy to understand, can approximate behavior rather well over small ranges of values, has one independent variable and one dependent variable, y=F(X)=a+bx y-independent, bx- dependent

Excels Regression Tool can be used for both:

simple and multiple linear regressions.

Residuals are the observed errors which are:

the differences between the actual values and the estimated values of the dependent variables.

Probability density functions:

the distribution that characterizes the outcomes of a continuous random variable.

Discrete random variable:

the numbers of a possible outcome can be counted. EX: the number of cars sold by a car dealer in one month The number of students who were protesting the tuition increase last semester The number of applicants who have applied for a vacant position at a company

joint p

the probability of the intersection of two events

Regression models of ______ data focus on predicting the future.

time-series

Regression models of ________ data focus on predicting the future.

time-series

The Delphi method used for forecasting:

uses a panel of experts, whose identities are typically kept confidential from one another, to respond to a sequence of questionnaires.

Variance is the

weighted average of squared deviations from the expected value common measure of dispersion Also measures the uncertainty of the random variable the higher this is, the higher the uncertainty of the outcome

Exponential function

y+abx

Time series that do not have trend, season, or cyclical effects but are relatively constant and exhibit only random behavior are called stationary time series.

True

Variance calculates the probability of a random variable lying within a certain interval.

True

Polynomial function:

A second-order polynomial is parabolic in nature and has only one hill or valley, a third-order polynomial has one or two hills or valleys. Revenue models that incorporate price elasticity are often polynomial functions.

Relative frequency definition:

Based on empirical data. The probability than an outcome will occur is simply it associated with that outcome. Ex: Distribution of computer repair times.

Subjective definition:

Based on judgement and experience. Ex: Sports experts might predict at the start of the football season.

cross sectional model

Carried out at a single point in time on a statistical unit

Logarithmic Functions

Constructed so that the successive points along an axis, or graduations are an equal distance apart, represent values which are in an equal ratio. are used when the rate of change in a variable increases or decreases quickly and then levels out, such as with diminishing returns to scale. y=m ln(x)+b

Classical definition of probability:

If the process generates the outcome is known, probabilities can be deduced from theoretical arguments. Ex: Rolling dice

dependent events

If whether or not one event does affect the probability that the other event will occur, then the two events are said to be dependent.

Excel's Trendline feature cannot be used in modeling trends which include time variables. Group of answer choices

False

Higher variance implies low uncertainty.

False

Linear functions are used when the rate of change in a variable increases or decreases quickly and then levels out, such as with diminishing returns to scale.

False

The expected value of a random variable corresponds to the notion of the median for a sample.

False

The standard error may be assumed to be large if the data are clustered close to the regression line.

False

The triangular distribution is defined by three parameters: the mean, median, and mode.

False

Exponential functions:

Have the property that y rises or falls at constantly increasing rates, example: A lightbulb brightness grows at a decreasing rate as the wattage increases Assume a>o, b>0, and not =1 if b>1, then you have exponential growth. As x inceases, outputs increase slowly at first, then increase more and more rapidly if 0<b<1, the function has exponential decay. As x increases, outputs decrease rapidly at first then level off y=ab^x

The mean absolute deviation (MAD) is the absolute difference between the actual value and the forecast, averaged over a range of forecasted values.

True

The mean, median, and mode are all equal in normal distribution.

True

The more scattered the data, the larger the standard error.

True

time series

Independant variable- time or function of time, focus is on predicting the future if one iv- simple regression if 2 or more- multiple regression

The normal distribution is a continuous distribution that is described by the familiar bell-shaped curve and is perhaps the most important distribution used in statistics.

True

The union of two events contains all outcomes that belong to either of the two events.

True

In Excel's Trendline tool:

Provides a convenient method for providing the best fitting functional relationship among these alternatives for a set of data.

normality of errors

Regression analysis assumes that the errors for each individual value of X are normally distributed, with a mean of zero. This can be verified by examining a histogram of the standard residuals and inspecting for a bell-shaped distribution or by using more formal goodness of fit tests. It is usually difficult to evaluate normality with small sample sizes.

Three major categories of forecasting approaches are qualitative and judgmental techniques, statistical time-series models, and explanatory/casual methods.

True

Mutually excl

The outcomes cannot be more than one event

marginal prob

The probability of an event, irrespective of the outcome of the other joint event

A good regression model has the fewest number of explanatory variables providing an adequate interpretation of the dependent variable.

True

A probability distribution is the characterization of the possible values that a random variable may assume along with the probability of assuming these values.

True

A random variable is a numerical description of the outcome of an experiment.

True

A versatile, yet highly effective, approach for short range forecasting is simple exponential smoothing.

True

Conditional probability is the probability of occurrence of one event 'A' given that another event 'B' is known to be true or already occurred.

True

Conditional probability is the probability of occurrence of one event 'A' given that another event 'B' is known to be true or has already occurred.

True

Creating a scatter chart with an added trendline is visually superior to the scatter chart generated by line fit plots.

True

Exponential functions have the property that y rises or falls at constantly increasing rates.

True

In predictive analysis models, a second-order polynomial has only one hill or valley.

True

It is usually difficult to evaluate normality with small sample sizes.

True

Mean square error (MSE) penalizes larger errors because squaring larger numbers has a greater impact than squaring smaller numbers.

True

Normal distribution is symmetric, so its measure of skewness is zero.

True

Observed errors can be positive or negative.

True

One judgmental approach for forecasting is historical analogy, in which a forecast is obtained through a comparative analysis with a previous situation.

True

Probability is the likelihood that an outcome occurs.

True

Qualitative and judgmental techniques rely on experience and intuition.

True

Random variables may be continuous or discrete.

True

Regression analysis is a tool for building mathematical and statistical models that characterize relationships between a dependent variable and one or more independent, or explanatory, variables.

True

Simple linear regression involves finding a linear relationship between one independent variable, X, and one dependent variable, Y.

True

Standard residuals (observed errors) are residuals divided by their standard deviation.

True

The Delphi method is a popular forecasting approach which uses a panel of experts to respond to a series of questionnaires.

True

The higher the variance, the higher the uncertainty of the outcome.

True

independent events

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.