Question 1

useful graphs

Accepted Answer

scatterplot
can get a sense for the nature of the relationship

Question 2

what to look for in a graph

Accepted Answer

relationship between two variables where one variable causes changes to another

Question 3

location

Accepted Answer

where most of the data lies

Question 4

spread

Accepted Answer

variability of the data, how far apart or close together it is

Question 5

shape

Accepted Answer

symetric, skewed etc

Question 6

nature of relationship

Accepted Answer

existent/ non-existent
strong/ weak
increasing/ decreasing
linear/ non-linear

Question 7

outliers in scatterplots

Accepted Answer

represent some unexplainable anomalies in data
could reveal possible systematic structure worthy of investigation

Question 8

casual relationship

Accepted Answer

relationship between two variables where one variable causes changes to another

Question 9

explanatory variable

Accepted Answer

explains or causes the change
on x-axis

Question 10

response variable

Accepted Answer

is changed
on y-axis

Question 11

useful numbers

Accepted Answer

correlation and regression

Question 12

formula for the correlation coefficient

Accepted Answer

r= 1/(n-1) ∑▒〖((xi-x ̅)/sx〗)((yi-y ̅)/sy)

Question 13

xi or yi

Accepted Answer

axis values of corresponding letter

Question 14

xbar or ybar

Accepted Answer

mean of axis values of corresponding letter

Question 15

sx or sy

Accepted Answer

standard deviation of axis values of corresponding latter

Question 16

properties of r

Accepted Answer

close to 1 = strong positive linear relatoinship
close to -1 = strong negative linear relationship
close to 0 = weak or non-existent linear relationsip

Question 17

cautions about the use of r

Accepted Answer

only useful for describing linear relationships
sensitive to outliers

Question 18

regression models

Accepted Answer

general linear relationships between variables

focus negative = decrease

Question 19

what regression modelling does

Accepted Answer

describes behaviour of response variable (the variable of interest) in terms of a collection predictors (related variables ie. explanatory variable(s))

Question 20

a linear framework is used to look at?

Accepted Answer

the relationship between the response and the regressors
formula: Y = α + βx
Where α is the intercept and β is the slope

Question 21

ideal model for linear framework in terms of responses and regressors

Accepted Answer

one unique response to one given regressor

Question 22

real world model for linear framework in terms of responses and regressors

Accepted Answer

must approximate

Question 23

statistical model

Accepted Answer

relates response to physical model predictions
allows for better predictions and quantification of uncertainty concerning the response
to make decisions

Question 24

what does regression analysis do?

Accepted Answer

finds the best relationship between responses and regressors for a particular class of models

Question 25

experimenter controls predictors, why?

Accepted Answer

may be important for making inferences about the effect of predictors on response

Question 26

course assumption

Accepted Answer

predictors are controlled in an experiment or at least accurately measured

Question 27

define a good statistical model

Accepted Answer

fit, predictive performance, parsimony interpretability

Question 28

qualitative description of model

Accepted Answer

response = signal + noise
Y = α + βx + ǫ
ǫ = noise

Question 29

define signal

Accepted Answer

a small number of unknown parameters
variation in response explained in terms of predictors
it is the systematic part of the model

Question 30

define noise

Accepted Answer

residual variation unexplained in the systematic part of the model
can be described in terms of unknown parameters

Question 31

what does a good statistical model do to possibly large and complex data

Accepted Answer

reduces it to a small number of parameters

Question 32

a model will fit well if

Accepted Answer

the systematic part of the model describes much of the variation in the response (low noise)
large number of parameters may be required to do this

Question 33

define parsimony:

Accepted Answer

smaller number of parameters = grater reduction of data, more useful for making a decision

Question 34

there is a cycle between what?

Accepted Answer

tentative model formulation, estimation of parameters and model criticism

Question 35

a good model will

Accepted Answer

manage balance between goodness of fit and complexity
provide reduction useful data

Question 36

model response variable in terms of a single predictor

Accepted Answer

yn = values of the response variable

2Qunatit

data analysis

Question	Answer
useful graphs	scatterplot can get a sense for the nature of the relationship
what to look for in a graph	relationship between two variables where one variable causes changes to another
location	where most of the data lies
spread	variability of the data, how far apart or close together it is
shape	symetric, skewed etc
nature of relationship	existent/ non-existent strong/ weak increasing/ decreasing linear/ non-linear
outliers in scatterplots	represent some unexplainable anomalies in data could reveal possible systematic structure worthy of investigation
casual relationship	relationship between two variables where one variable causes changes to another
explanatory variable	explains or causes the change on x-axis
response variable	is changed on y-axis
useful numbers	correlation and regression
formula for the correlation coefficient	r= 1/(n-1) ∑▒〖((xi-x ̅)/sx〗)((yi-y ̅)/sy)
xi or yi	axis values of corresponding letter
xbar or ybar	mean of axis values of corresponding letter
sx or sy	standard deviation of axis values of corresponding latter
properties of r	close to 1 = strong positive linear relatoinship close to -1 = strong negative linear relationship close to 0 = weak or non-existent linear relationsip
cautions about the use of r	only useful for describing linear relationships sensitive to outliers
regression models	general linear relationships between variables focus negative = decrease
what regression modelling does	describes behaviour of response variable (the variable of interest) in terms of a collection predictors (related variables ie. explanatory variable(s))
a linear framework is used to look at?	the relationship between the response and the regressors formula: Y = α + βx Where α is the intercept and β is the slope
ideal model for linear framework in terms of responses and regressors	one unique response to one given regressor
real world model for linear framework in terms of responses and regressors	must approximate
statistical model	relates response to physical model predictions allows for better predictions and quantification of uncertainty concerning the response to make decisions
what does regression analysis do?	finds the best relationship between responses and regressors for a particular class of models
experimenter controls predictors, why?	may be important for making inferences about the effect of predictors on response
course assumption	predictors are controlled in an experiment or at least accurately measured
define a good statistical model	fit, predictive performance, parsimony interpretability
qualitative description of model	response = signal + noise Y = α + βx + ǫ ǫ = noise
define signal	a small number of unknown parameters variation in response explained in terms of predictors it is the systematic part of the model
define noise	residual variation unexplained in the systematic part of the model can be described in terms of unknown parameters
what does a good statistical model do to possibly large and complex data	reduces it to a small number of parameters
a model will fit well if	the systematic part of the model describes much of the variation in the response (low noise) large number of parameters may be required to do this
define parsimony:	smaller number of parameters = grater reduction of data, more useful for making a decision
there is a cycle between what?	tentative model formulation, estimation of parameters and model criticism
a good model will	manage balance between goodness of fit and complexity provide reduction useful data
model response variable in terms of a single predictor	yn = values of the response variable

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