Midterm 2

Question 1

What are the consequences of violating these assumption?

Answer 1

P-values will not be meaningful

Parameters may not be accurate

Question 2

What is independence?

Answer 2

Knowing the error of one or a subset of datapts provides no knowledge of the error of any others

Question 3

What are the 3 ways non-independence arises?

Answer 3

Heterogeneity in the dataset (ignoring natural subsets related to response
Replicate measurements per test subject incorrectly inflates dfresidual
Nested data( ignoring subs smoking or another hierarchy caused heterogeneity in data

Question 4

What are 3 warning signs of non-independence in a study?

Answer 4

Too many data points
Indication of any kind of repeated measurements
Any implausible result

Question 5

What is homogeneity of variance?

Answer 5

Assumption that the scatter around old he model is of equal magnitude throughout the fitted model

Question 6

What is the ideal approach for homogeneity of variance?

Answer 6

Residuals spread equally above and below fitted line. Plot residuals~ fitted values

Question 7

What is normality of error?

Answer 7

When the residuals are normally distributed

Question 8

Which type of plot is a more of a precise way to visualize distribution normality??

Answer 8

QQ Norm. If the QQnorm plot fits a straight line between -2 and +2 then the data is normally distributed

Question 9

What is the Shapiro-will test

Answer 9

It test for normality giving a specific p-value for the null hypothesis that the data is normally distributed

Question 10

How do we fix non normality and inhomogeneity?

Answer 10

Transform the variables. Ex apply log, sqrt, or exp

Question 11

If residuals~ frequency plot is a right hand tail how do we fix the problem

Answer 11

Transform the response variable with log, sqrt or 1/y.

Question 12

If residual~frequency is a left hand tail, how do we fix the problem

Answer 12

Transform the variable with e^y

Question 13

What is linearity/additivity

Answer 13

A linear relationship between the response and the explanatory variables

Question 14

How is non linearity detected

Answer 14

Plot the residuals against each of the explanatory variable. If linear the plot for each variable should show an equal distribution of points above and below zero

Question 15

What other strategies to fix non-linearity

Answer 15

Inclusion of variable interactions

Inclusion of higher powers of the explanatory variables

Question 16

What is model criticism

Answer 16

Testing key assumption of general linear models
Be normally distributed with mean zero
Not systemically vary different values of he predicted response
Not systematically vary for different values of any of the explanatory variables

Question 17

From a scientific understanding what is conflicted a best model

Answer 17

Fewest explanatory variables that yield model who small p-value

Question 18

An accurate predictive model is considered a beat model of?

Answer 18

Highest r^2 without regard for number variables but avoid over-fitting

Question 19

What are the three principles of model choice

Answer 19

Economy of variables
Considerations of mariginality
Multiplicity of p-values

Question 20

What is economy of variables

Answer 20

The simpler the better

Question 21

What is multiplicity of p values

Answer 21

If you calculate enough p values some models will be significant just be chance

Question 22

What is considerations of marginality

Answer 22

The simplest terms have priority and inclusion of interaction terms requires the inclusion of their simpler parts

Question 23

What is the goal of economy of variables

Answer 23

To identify the minimum adequate model

Question 24

How to deal with the problem of multiplicity of p values

Answer 24

Reduce the p value cutoff
Use more specialized statistical tests
Reduce the number of explanatory variables by combining multiple terms into a single term
Focus, don’t fish

Question 25

What is the importance of marginality

Answer 25

Hierarchies must be respected in model formulae

Question 26

How is type 4 goal of finishing the subset of variable to explain some response achieved?

Answer 26

1. Attempt to build a model using all first, second and third order terms 2. Build simpler model including only first and second order terms 3. Build simpler models removing terms not deemed significant 4. Build simpler model including only first order terms

Question 27

What is adjusted r^2

Answer 27

One metric for measuring how "economically" a model describes a data set of rules

Question 28

What is the formula for adjusted R^2

Answer 28

(Total MS-Residual MS)/ total MS where total MS= total ss/total df 1 + ( R^2-1) (dftotal/(df total-df model)

Question 29

How to determine how "economically" a model describe a data set

Answer 29

1. Use adjusted r^2 | 2. Use prediction intervals (increases as you add insignificant explanatory variables

Question 30

What are possible pitfalls with automated methods

Answer 30

Temptation just to let the computer do the thinking and neglect other relevant info Slightly different automated procedure can give different models Don't take overall p value of final model too literally

Question 31

What is a stepwise regression

Answer 31

An automated procedure for selecting a subset of variables in a model Backwards stepwise regression Forward stepwise regression

Question 32

What is a backward stepwise regression

Answer 32

Build full model and remove that variable that contributes that lease Build new model and remove variable that contributes least y~x1+ x2+x3

Question 33

What is forward stepwise regression

Answer 33

y~X1 y~x2 y~3 Y~x3+x1. Y~x3+x2 Stop when additional variable does not improve adjusted r2

Question 34

What is akaike information criterion (aic)

Answer 34

Alc= nln(rss/n) + 2k Lower aic means better model

Question 35

What is the purpose of addingrandom effects

Answer 35

Random effects add a new type of variance to estimate Estimate how the individual to individual variation compares to the variation due to other effects

Question 36

What does nested data allow us to quantify

Answer 36

Random effects

Question 37

What is population modeling?

Answer 37

The use of property of individual to predict future populations

Question 38

What is "r"

Answer 38

The net reproduction per individual per unit time R= birth rate(f)- death rate (d)

Question 39

What is the Malthusian model

Answer 39

Change of p= r*p P(t+1)= p(t) + r* p(t)

Question 40

In the Malthusian model what are the behaviors of r?

Answer 40

r> 0 deltaP>0 pop grows R=o deltaP= constant R

Question 41

What is the total fertility rate (tfr)

Answer 41

The average number of children born per women over her lifetime

Question 42

What is carrying capacity (k)

Answer 42

Maximum number of individual that can be sustained in a particular habitat

Question 43

What is logistic growth

Answer 43

This occurs when population size is limited by carrying capacity

Question 44

What is the logistic model equation

Answer 44

``` deltaP= rmax * p(1-p/k) this creates a parabola Where r= max pop growth rate K= carrying capacity P= number of individuals DeltaP= pop growth/ unit time ``` P(t+1)= P(t) + rmax*P(t)(1-Pt/k)

Question 45

What is the behavior of K in a logistic model

Answer 45

When P> K then delta deltaP

Question 46

What are control structures

Answer 46

Manage how many times commands in a program are executed

Question 47

What are loops

Answer 47

Run a set of commands a specified number of times until some condition is true

Question 48

What are conditional

Answer 48

Run a set of commands not if some condition is true

Question 49

What is the "for" command used for

Answer 49

To repeat a set of commands a set number of times Ex. For( I in 1:10) { print(i)}

Question 50

How to use a loop to add up a list of numbers

Answer 50

Use the counter command Counter

Question 51

How to loop a vector

Answer 51

Vector

Question 52

How do we determine population model parameters

Answer 52

Fit the model to real data

Question 53

How automate the processing of optimizing the values of r and k

Answer 53

Define the fitness to be minimized

Question 54

What are equilibrium points

Answer 54

Occur where the values are unchanged between time steps This can be determined by setting both the Malthusian and logistic model p or k=0

Question 55

What determine stability of equilibrium points

Answer 55

Perturbation analysis algebraically or graphically Substitute Pt= P* + Pt

Question 56

When does equilibrium occurs

Answer 56

P(t+1)= F(Pt) = Pt F(P) > 1 unstable F(P)

Question 57

What is the stretching factor

Answer 57

(1+rmax) pt tells of theres shrinkage or growth

Question 58

What type of diagram will indicate whether the model converged to an equilibrium point

Answer 58

A cobweb diagram

Question 59

In the logistic model on perturbation analysis when is are the conditions when r> 0

Answer 59

0

Question 60

Perturbation analysis when r

Answer 60

-1

Question 61

What leads to chaotic behavior

Answer 61

Increasing r values leads to first oscillatory | The bifurcation diagram shows chaotic behavior

Question 62

What is the Ricker model

Answer 62

Pt+1= pt* e^rmax(1-pt/k) | Never produces negative populationd but is noiser than logistic model

Question 63

What are the four assumptions?

Answer 63

Independence Normality of error Homogeneity of variance Linearity/additivity