Test 2

The linear correlation coefficient is ALWAYS between _______ and ______.

-1, 1

If disjoint the probability is _____

0

The coefficient of determination is a number between ______ and _____

0, 1

The probability of any event E, P(E), must be greater than or equal to ____ and less than or equal to ____

0, 1

The probability of any event must be between _____ and ____

0, 1

The sum of probabilities of all outcome must equal ____

1

The sum of probabilities of all outcomes in the sample space must equal ___

1

If something is less than ___% it is unusual.

5

x and y plays __________ ___________ in the interpretation of r.

NO ROLE

Pattern =

NOT appropriate

The probability that two events E and F both occur is P(E and F)=

P(E)*P(E|F)

If E and F are disjoint events then P(E or F) =

P(E)+P(F), add probabilities

If E and F are not disjoint then

P(E)+P(F)-P(E and F)

If an experiment has n equally likely outcomes and if the number of ways that an event E can occur is m then the probability of E is

P(E)=m/n

__________ is a measure of the likelihood of a random phenomenon or chance behavior

Probability

_____% change in y can be explained by the change in x

R

________ ________ represents a situation in which an association between two variables inverts or goes away when a third variable is introduced to the analysis

Simpson's paradox

If E and F are disjoint then ______ probabilities

add

No pattern =

appropriate

A high correlation DOES NOT imply ____________

causation

If an event is a ______, the probability of the event is 1

certainty

The _________ __ __________ (R²) measures the proportion of total variation in the response variable that is explained by the least squares regression line

coefficient of determination

A ________ ________ lists the relative frequency of each category of the response variable, given a specific value of the explanatory variable in the contingency table

conditional distribution

The strict requirement of the linear model being violated is called ________ __________ ________

constant error variance

A table that related to two categories of data is called a ______ _______ or ______ ____ _______

contingency table, two way table

Tow events are __________ if the occurrence of E in a probability experiment affects the probability of event F.

dependent

Two event are ______ if they have no outcomes in common

disjoint

So r close to 0.....

does not imply no relation just no linear relation

An _______ is any collection of outcomes from a probability experiment.

event

________ are what we are trying to find the probability of

events

In probability an __________ is any process that can be repeated in which the results are uncertain

experiment

The difference between the predicted value of the response variable and the mean value of the response variable is called the ________ _________

explained deviation

If R²=1 means that the line _______ _______ __ ___ _______ _______ _______ _______ ______.

explains 100 percent of the variation in the response variable

P(E)=relative frequency of E=

frequency of E/number of trials of experiment

The statistical term for constant error variance is ________________

homoscedasticity

The explanatory variable is plotted on the _________ _____________.

horizontal axis

If an event is ______, the probability of the event is 0

impossible

As the number of repetitions of a probability experiment ________, the proportion with which a certain outcome is observed gets _______ to the probability of the outcome

increases, closer

Two events E and F are _________ if the occurrence of event E in a probability experiment DOES NOT affect the probability of event F.

independent

An _________ _________ is an observation that significantly affects the least squares regression lines slope and/or y intercept or the value of the correlation coefficient

influential observation

The experiment is a binomial experiment if ...

it is performed a fixed number of times, trials are independent, there are two mutually exclusive (disjoint) outcomes (success or failure), probability is fixed for each trial

The ___________ __________ ________ _________ is a line that minimizes the sum of squared errors (or residuals)

least squares regression line

The ___________ __________ __________ ______ minimizes the sum of the squared vertical distance between the observed values of y and those predicted by the line (y-hat)

least squares regression line

To determine R² for the linear regression model simply square the value of the _________ _________ _________.

linear correlation coefficient

The _____________ _______________ ______________ or ______________ _________ ___________ __________ _________ a measure of the strength and direction of the linear relation between two quantitative variable.

linear correlation coefficient, Pearson product moment correlation coefficient

If r is close to 0 then _________ to _________ evidence exists of a linear relation.

little, no

The ______ _______ _______ in which a certain outcome is observed is the probability of that outcome

long term proportion

A ____________ _________ is related to both the explanatory and response variable.

lurking variable

Another way that two variables can be related even though there is not a causal relation is through a _________ _________.

lurking variable

A ___________ __________ of the variable is a frequency (tally marks) or relative frequency (percentages) distribution of either the row or column variable in the contingency table

marginal distribution

If a plot of the residuals against the predictor variable shows a discernible pattern such as a curve, then the response and predictor variable _______ _______ ______ _______ ________

may not be linearly related

IF independent event _______ probabilities

multiply

Disjoint events are also referred to as _______ ________ events

mutually exclusive

The closer r is to -1 the stronger the evidence of ____________ association between two variables.

negative

If R²=0 means the line has _____ _____ _______.

no explanatory value

The correlation coefficient is ___________ _________.

not resistant

If S is the sample space of this experiment, P(E)=N(E)/N(S) where N(E) is the ____________ and N(S) is the

number of outcomes in E, number of outcome in sample space

An event may consist of _____ outcome or ____ _____ _____ outcome.

one, more than one

Probability describes the long term proportion with which a certain ________ will occur in situations with short term uncertainty

outcome

Residuals help to check for ___________

outliers

If r= -1 then a ____________ ____________ __________ __________ exists between two variables.

perfect negative linear relation

If r= +1 then a ________ ____________ _______ _______ exists between two variables.

perfect positive linear relation

the closer r is to +1 the stronger the evidence of ___________ association between the two variables.

positive

Residuals help to determine whether a linear model is appropriate to describe the relation between the __________ and __________ ___________

predictor, response variables

A __________ ________ provides the possible values of the random variable X and their corresponding probabilities

probability distribution

A ______ ______ lists the possible outcomes of a probability experiment and each outcomes probability.

probability model

A _______ ________ is a numerical measure of the outcome from a probability experiment so its value is determined by chance.

random variable

_____________ play an important role in determining the adequacy of the linear model

residuals

The ___________ variable is the variable whose value can be explained by the value of the ______________ variable.

response, explanatory

A probability model must satisfy all of the ______ ___ _______.

rules of probabilities

r represents the _________ ____________ _________.

sample correlation coefficient

The ____ ________ (S) of a probability experiment is the collection of all possible outcomes.

sample space

A ___________ __________ diagram shows the relationship between two quantitive variable measured on the same individual.

scatter diagram

Probability deals with experiments that yield random __________ ________ ________ or results yet reveal _______ ________ __________

short term outcomes, long term predictability

Events with one outcome are sometimes called ______ events.

simple

__________ _________ is based on your opinion

subjective probability

The notation P(F|E) is read "______________"

the probability of even F given event E

The difference between the the observed value of the response variable and the mean value of the response variable is called ___________ ________

total deviation

The difference between the observed value of the response variable and the predicted value of the response variable is called the _________ ________

unexplained deviation

The linear correlation coefficient is __________.

unitless

An _________ event is an event that has a low probability of occurring

unusual

Residuals help to determine whether the __________ of the residuals are constant

variance

The response variable is plotted on the ____________ __________.

vertical axis

If a plot of the residuals against the explanatory variable shows the spread of the residuals increasing or decreasing as the explanatory variable increases then a strict requirement of the linear model is _________

violated

change in y can be explained by ___

x

The equation for the least squares regression line is given by

y=b₁x+b₀