MIS 301 Quiz 3 Shaul SDSU

ANOVA

Analysis of variance. A statistical procedure examining variations between two or more sets of interval or ratio data.

for an ANOVA test what is the numerator of the variance

the basis of the test

with each ANOVA test

our probability of making a type 1 error increases

type one error

rejecting null hypothesis when it is actually true - a false positive

type 2 error

failing to reject a false null hypothesis

TS > CV

reject null

TS < CV

fail to reject null

assumptions of ANOVA Test

the null is true

at least interval level data

the Central Limit Theorem is Satisfied

random independent samples

the variances are equal

ANOVA factor/classification/treatment

overarching title on how our data is organized

ANOVA categories

nominal level data that identifies a group

criterion variable

the actual numerical values

ANOVA data variation

within and betweem

ANOVA Data Variation : Within

due to chance, randomness and error

ANOVA Data Variation: Between

due to factor/classification/treatment

ANOVA: Distance from x to x double bar is

sum of squares total or total variation

ANOVA: distance from x to x bar is

sum of squares between or variation due to factor

ANOVA: distance from x bar to x double bar

sum of the squares within or variation due to chance

Underlying theory of ANOVA Test

total variation can be portioned into 2 parts- within and between, and those two components can be compared to determine which is affecting the data at a greater degree

ANOVA formula for test stat

Between Term/ Within Term

ANOVA: large test stat means

more likely to reject the null because the factor is affecting the data

ANOVA: small test stat means

more likely to fail to reject because the variation is due more to chance than the factor

bivariate data

Data with two variables

multivariate data

More than two variables are measured on a single experimental unit.

time series

a time-ordered sequence of observations taken at regular intervals

cross section

variation across units of observation during one point of time

panel data

information collected from a group of consumers, organized into panels, over time

r

sample correlation coefficient

The value of r is always between

-1 and 1

the size of the correlation r indicates...

the strength of the linear relationship of x1 and x2

values of r close to 1 or -1 indicate

strong correlation

if r is 0

there is no correlation

if r is 1

there is a perfect positive correlation- when x1 increase, x2 increase

if r is -1

there is perfect negative correlation- when x1 increase x2 decrease

for correlation, data is compared to ______ then to ______

compared to their means then to each other

sample size needed for correlation

10 data points for x and 10 for y

relationships change

over time, outside the data, and across space

correlation leads to

causation then liability, opportunity, or beneficiary

a high r does

not always mean we need to reject the null

sample size effect

as sample size increase, r significance goes down

if r is significant and strong correlation

it is useful

if r is not significant, and weak correlation

it is not useful

if r is not significant and the correlation is weak

it is not useful

if r is significant but weak correlation

it is not useful

if r is significant and moderate correlated

it could be useful

simple linear regression

regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line

error for SLR is

actual value- predicted value

total variation in y can be broken into two variables

residual term and regression term

residual term

y's relationship with the x variable

regression term

random factors not in the model- error

four concepts of slr

1. the coefficient of determination

2. isolating the slope: effect of marginal inputs on the outputs

3. over and underperforming the model (y above the line, positive e, over performing; y below the line, negative e, under performing)

4. Restricted model: some predictor variables

alpha > p value

reject the null

alpha < p value

fail to reject null

line of best fit

the regression line that best fits the observed data and minimizes the error in prediction

properties of residual error

if r = +/-1, e= 0, ordinarily, least squares regression pulls down total error

df

degrees of freedom

SS

sum of squares

MS

mean square

F

test stat

F=

MS regression/ MS residual

as the predictor variable increase

the adjusted r squared drops, so you can't just keep adding more predictor variables to drive up multiple r because r square will be penalized

if the general rule regarding sample size is not met...

adjusted r squared is a better measurement of regression strength

as shared variation between the x variable and the y variable increases

r approaches it's upper and lower limit respectfully

significance f =

p-value

dummy variable

A variable for which all cases falling into a specific category assume the value of 1, and all cases not falling into that category assume a value of 0.

collinearity check

if r is greater than or equal to .6, be concerned

if r is greater than or equal to ,8, there is a collinearity error

for a multivariate regression

R is always positive, does not suggest the direction of the relationship, R is greater than or equal to any single X-Y relationship, R is a single value representing the strength of a simultaneous relationship between the x variables and the y variables

Multiple Regression population notation

β0

Multiple Regression partial correlation coefficient sample notation

β1

Collinearity

when 2 or more x variables are highly correlated with each other

Y hat

predicted value

y bar

chance model

DFregression

k-1

DFresidual

nt-k

DFtotal

nt-1

high MS regression/ low MS residual

F is high, probs gonna reject null

low ms regression/ high ms residual

low f, prob gonna fail to reject

ANOVA table tells us

whether or not the model is a good one- reject= a good model, FTR = a bad model

regression stats tell us

multiple r which tells us the level of correlation between the x variable and y

coefficient table

tell us the significance of each component- FTR = the x variable is not a good predictor, reject= the x value is a good predictor

the ANOVA table is a ____ question

stat question

the coefficient table is a _____ question

stat question

as collinearity decreases, there is an increase in

each predictor variable's unique position of the variability within the y variable

y below the line

negative e, under performing

y above the line

positive e, over performing

when p is low

reject Ho

regression stat table is a _____ question

judgement

when n goes up

ms residual goes down

when ms residual goes down

the test stat goes up