chemometrics quiz 2

Question 1

bicariate vs multivariate

Answer 1

bivariate looks at two data sets and tells how related - multivariate explains relationship between more than 2

Question 2

Covariance vs correlation

Answer 2

Covariance - how two data sets change or vary together in tandem
Correlation - tells you when a change in one variable leads to a change in another

Question 3

How do you calculate covaariance

Answer 3

Take mean of x and y
Take each point and subtract its x and y from their respective means and sum up
then divide by N-1

Question 4

Scales of covariance vs correlation

Answer 4

covariance affected by change in scale - correlation isn’t
covariance keeps units correlation doesn’t
each are - when the two are independent
covariance from infinity to negative infinity correlation is from 1 to -1

Question 5

How to calculate correlation

Answer 5

Covariance divided by (stdev x *stdev y)

Question 6

how to program these

Answer 6

cor and cov

Question 7

whats a corrgram

Answer 7

correlation matrix so basically the same variables on x and y axis s and see how they correlate, can be picture or colored etc - match top and bottom typically show how much and in what direction

Question 8

How do p alues work with correlation

Answer 8

p vallue < 0.05 means correlation coefficient different than 0

Question 9

Whats a scatter plot matrix?

Answer 9

same idea as a corrgram but each space has an actual scatter plot

Question 10

How do you plot scatter plot matrix

Answer 10

pairs() funcion

Question 11

Partial Correlation

Answer 11

between two quantitative variables - controlling for one or more quantitative variables

Question 12

WHat is regression used for

Answer 12

1) IDing explanatory variables that are related to an outcome/response variable
2) Describe the form of a relationship between dependant and independent variable (general relationship()
3) Provide an equation to predict response variable from explanatory variable (cal curve)

Question 13

Ordinary least squares regression what is it

Answer 13

quantitative depedant variable predicted from a weighted sum of predictor variables where weights are parameters estimated from data

Question 14

goal of regression

Answer 14

choose model paramteres (Y and B! sloe and intercept) - that minimize difference between actual and predicted model

Question 15

What is a residual

Answer 15

the difference between the observed and fitted value

Question 16

what is true about sum of residuals

Answer 16

in a linear regression model - sum of residuals should be 0

Question 17

Wghat determines best fit

Answer 17

minimize sum of squared differences

Question 18

ASSUMPTIONS FOR LINEAR REGRESSION

Answer 18

Error in your x should be negligible
Error with y vlue must be normally distributed (dependant variable needs to be normally distributed)
Varian in error across y should be constant across area of interest (stdev constant)
x and y should be continuous

Question 19

Whats a high leverge point and how to deal

Answer 19

a point that has more influlence on r^2
can deal with by having event spaced values

Question 20

How to calculate regression

Answer 20

determine residuals then calculate residual standard dev - deviation of data points form regression line
stdev for slope
stdev for y intercept ( y - y fitted) squared and then summed

Question 21

How to insepct residuals

Answer 21

plot them - should be scattered around zero with no pattern

Question 22

How to tell how influential a data point is

Answer 22

COOKS DISTANCE -

Question 23

How do t test and p vallue relate to regression

Answer 23

if p value less than 5 - significantly different than - THERE IS A RELATIONSHIP

Question 24

R^2

Answer 24

shows how well the points fit

Question 25

How to test your prediction analysis

Answer 25

Make the regression with 80% while saving 20% to test afterwards ( split randomly

Question 26

What is the minmax and MAPE

Answer 26

min max accuracy and MEAN ABSOLUTE PERCENT ERROR
- tells you how far its off from a perfect model (1 is perfect)
MAPE same thing - MAPE is 10 on average if forecast off by 10% its 100-MAPE (eg a MAPE of .49 means its 51% accurate

Question 27

POLYNOMIAL REGRESSION (2nd order)how does it change

Answer 27

instead of y= a + bx
y = a +bx + cx^2

Question 28

What is multiple linear regression used for

Answer 28

When ou have more than one predictor variable - eg the more predictors the more - cubic is 3

Question 29

how to interpret regression slope

Answer 29

basically the slope indicates change in one variable in comparison to another
eg increase in dependant variable for one unit of the independent

Question 30

Confidence interval for regression

Answer 30

95% confidence interval says 95% confident that the interval contains the true value
AHH - so we’re predicting right - 95% confidence says the actual value is between these ranges vs just an absolute here’s this value

Question 31

How do you test if dependant variables are independt

Answer 31

DURBIN WATSON

Question 32

What is global validation

Answer 32

a test that performs a variety of tests to see if regression is valid
skew, urotsis, equal variancesetc

Question 33

How to test for outliers

Answer 33

outlierTest() gives bonferroni adjusted pvalue

Question 34

what is hat statistics

Answer 34

hat tells you if theres a high leverage point (is an unusual combination) - can set the statistic and plot 2 or 3 times hat and see where things end up
p/n (p is number of parameters in model
including intercept and n is sample size

Question 35

What is an AV plot

Answer 35

added variable plot another way to test for influential points

Question 36

What is an influence plot

Answer 36

shows outliers LEVERAGE and influential observations in one plot - size is the influence, shows hat value on one

Question 37

What are corrective measure if ID problesm with regression

Answer 37

delete observations, transform variables, add or delete variables, change approach

Question 38

What is a nested model for

Answer 38

to look at multiple predicotrs and see which one does the best job to explain

Question 39

What is AIC

Answer 39

Akaike information criteriion - again takes into account eh models fit - a smaller value is preferred (can take in multiple predictors or less and show whats better fit