lecture 19,20,21

Question 1

what is a multinomial experiment?

Answer 1

qualitative data falling into more than 2 categories

Question 2

properties of a multinomial experiment?

Answer 2

n identical trials
k possible outcomes (categories or cells)
probabilities are p1, p2, p3 and remain the same from trail to trial
independent trials
random variable interests are cell counts, n1, n2, of the # of observations that fall in each of the k classes

Question 3

what is a one way table

Answer 3

consider a multinomial experiment with k outcomes that correspond to categories of a single qualitative variable. These results are summarized in a one way table

one way because only one variable is classified

Question 4

what does a chi sqaured test measure?

Answer 4

the degree of disagreement between the data and null hypothesis

Question 5

5 steps to solving a chi squared?

Answer 5

1 state null and alternative
2 test statistic (x^2= sum of (ni-npi,0)^2/npi,0)
3 Specify a
4 calculate test stat
5 determine whether to fail to reject or reject null and draw conclusions

Question 6

rejection region for chi squared?

Answer 6

if x^2> x^2a, k-1; where k-1 is number of cells -1

Question 7

conditions for x^2

Answer 7

multinomial experiment; satisfied by taking a random sample
n is large; satisfied if for every cell, Ei>5

Question 8

what is the chi squared used to determine?

Answer 8

whether there is a significant difference between expected frequencies and observed frequencies in one or more categories

Question 9

what is a two way contigency table?

Answer 9

multinomial experiment results summarized in 2-way table called a contigency table
probability totals are called marginal probabilites for each row and column

Question 10

what happens in a contingency table analysis?

Answer 10

if the two classifications are independent, the probability that an item is classified in any particular cell of the table is the product of the corresponding marginal probabilities.

Question 11

how to estimate probabilites?

Answer 11

phatci= Ri/n
phatci=Ci/n

Question 12

as the number of degrees of freedom increases,?

Answer 12

the chi squared distribution becomes more symmetrical; values of x^2 are always positive. The distributions are positively skewed

Question 13

finding expected cell counts for 2-way table

Answer 13

Ehat=RiCj/n

Question 14

test stat for two way table?

Answer 14

x^2= sum of (nij-Ehatij)^2/Ehatij

Question 15

pvalue

Answer 15

P(x^2>x^2a) where x^2a has (r-1)(c-1) df and x^2c is computed value of test stat

Question 16

conditions for a contingency table?

Answer 16

1 n observed counts are random sample from population of interest. then consider it a multinomial experiment with rxc possible outcomes
2 n is large enough so that for every cell the estimated expected count, Ehatij is > 5; if not the approximation can become very poor

Question 17

what should happen if x^2 values does not exceed critical value of x^2

Answer 17

do not accept hypothesis of independence; avoid inferring a casual relationship between classifications.

Question 18

what can not be established by a contingency table?

Answer 18

The existence of causality cannot be established by a contingency table

Question 19

what is simple linear regression?

Answer 19

suppose we want to study the relationship between the dependent variable y and the predictor variable x. Suppose the equation has some restricted form such as y=Bo +B1x where Bo is the y intercept and B1 is the slope. This is known as a deterministic model

Question 20

if we use a model that accounts for random error…?

Answer 20

this is a probabilistic model which includes both a deterministic component and a random error component
y (variable of interest; we always assume that the mean value of random error =0 Therefore, E(y) is deterministic component)=deterministic component and random error

Question 21

what is the random error term?

Answer 21

E (y=Bo +B1x +E)

Question 22

what is x and y?

Answer 22

x= predictor, explanatory, or independent variable
y=response, outcome, or dependent variable

Question 23

what is the implication of linear regression?

Answer 23

expected value of Y is a linear function of x. Y differs from its expected value by a random amount
formally, let x, denote a particular value of the independent variable x, then our linear probabilistic model says
E(y|x1)=uy/x=mean value y when x is x1

Question 24

steps for linear regression?

Answer 24

1 hypothesize the deterministic component of model that relates the mean, E(y), to independent variable x
2 use sample data to estimate unknown parameters in model
3 specify the prob distribution of random error term and estimate the SD of this distribution
4 statistically evaluate the usefulness of the model
5 when satisfied that the model is useful, use it for prediction, estimation, and other purposes

Question 25

what is the least squares method?

Answer 25

determine the values for the parameters so that the overall discrepancy D= sume of (observed response-predicted response)^2 is minimized