new UNIT 7 stuff

Question 1

What are the three chi-squared models?

Answer 1

goodness of fit, test for homogeneity, test for independence

Question 2

When do you know it is GOF test?

Answer 2

When you have ONE ROW or ONE COLUMN.

then it gives you a ratio , like 1:2:5 or it gives you expected percents.

Question 3

how do you find expected count if n=25 for a 1:3:1 ratio? What test is it?

Answer 3

GOODNESS OF FIT
find total: 1+3+1 = 5
divide all by five and that gives exp percents
1/5 : 3/5 : 1/5
.20 : .60   :.20
now multiply each by n and get expected counts.
Almost always not a whole number.
25(.20) : 25(.60) :25(.20)

Question 4

How to find expected cell count on a matrix?

Answer 4

ROW TOTAL* COLUMN TOTAL/ OVERALL TOTAL

Question 5

What is diff between homogeneity and test for independence?

Answer 5

homogeneity is more than one sample and asking about one variable, independence is just one sample with two variables.

Question 6

what is df for goodness of fit?

Answer 6

cells - 1

Question 7

what is df for chi squared homogeneity or independence?

Answer 7

(rows-1)(columns - 1) (remove a row and a colunmn an count the cells that are left)

Question 8

what are the conditions for chi squared?

Answer 8

counts, five or more in each expected, independent (random), <10%

Question 9

what are the conditions for inference for slope? (hyp test or confidence interval for slope?)

Answer 9

straight enough (check residuals for random scatter), random and independent, and look at the HISTOGRAM OF THE RESIDUALS and make sure they are unimodal and symmetric

Question 10

How do you make a confidence interval with computer output?

Answer 10

STAT +/- CRIT SE The STAT and SE are given side by side in the output
the t crit is stilll INVT(area 1 tail, n-2),
Just put the +/- t crit between the actual slope and the given std. error. The calculation is simple

Question 11

With regression computer output, how do you find the p-value for hypothesis test with null: slope=0

Answer 11

p value is given at the end of the row that the slope is in! It is the SLOPE/SE
(because the t is [slope - 0)/ SE]

Question 12

With regression computer output, how is the t-ratio and the p-value calculated?

Answer 12

T ratio is just SLOPE/ST ERROR and the p value is just TCDF(T ratio, 9999, n-2)

Question 13

How do you find Expected Count?

Answer 13

for GOF: Expected % times (total)..

For indep and homog: ROW*COL/TOTAL

Question 14

What are conditions for chi squared?

Answer 14

indep, rand, <10%, 5 or more in EXPECTED cells

Question 15

when do you have to check conditions?

Answer 15

In all inference procedures:
ANY CONFIDENCE INTERVAL OR HYPOTHESIS TEST
(including chi squared and slope stuff)

Question 16

For the following output for the association between test score and amount of time studied, what is the equation of the LSRL?
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 16

Score HAT = 45.3 + 5.82 (hours studied)

Question 17

For the following output for the association between test score and amount of time studied, Create and interpret a 95% confidence interval for slope.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 17

STAT +- CRIT (SE)
5.82 +- CRIT (2.66)
crit is just INVT(.025, 73)
df is n-2 for regression!!

Question 18

For the following output for the association between test score and amount of time studied, Test a hypothesis to see if there is a significant association between time studied and test score.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 18

Ho: B1 = 0
Ha: B1 not= 0 BE SURE THEY ARE BETAS (Greek B’s)
small b is a sample slope, Beta is population slope
p value is given (.0159)… just interpret it!

Question 19

For the following output for the association between test score and amount of time studied, Interpret the slope in context.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 19

On average, for each hour a student studied more than another student, their test scores were about 5.82 points higher.

Question 20

For the following output for the association between test score and amount of time studied, interpret the r-squared in context.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 20

77.5% of the variability in test score can be explained by the model with hours studied.

Question 21

For the following output for the association between test score and amount of time studied, interpret the S in context.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 21

S is the standard deviation of the residual, or the typical residual. It is how far off we expect our actual data value to be from the model (from the predicted value). In context: We can expect our actual test score to be about 7.7 points off from the test score predicted by our model, based on the amount of time we studied.

Question 22

For the following output for the association between test score and amount of time studied, interpret the y intercept in context.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 22

The model predicts that a person who doesn’t study at all will score about a 45.3 on the test.

Question 23

For the following output for the association between test score and amount of time studied, What is the “5.82?”
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 23

That is the slope.

Question 24

For the following output for the association between test score and amount of time studied, where does the “t stat” column info come from?
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 24

T stat is the T score, the test statistic for null=0:
(STAT-NULL)/SE
(45.3 - 0) / 4.3 = 10.53
(5.82-0) / 2.66 = 2.189

Question 25

For the following output for the association between test score and amount of time studied, Where does the “p” column come from?
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 25

The p is the p value from a hypothesis test assuming the y intercept and the slope are zero. If you put those T-STATS into tcdf, you get the p values from this column.

Question 26

For the following output for the association between test score and amount of time studied, make a 90% confidence interval for the predicted score for someone who studied for 8 hours.
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 26

To make an interval for prediction, plug 8 into equation..  45.3 + 5.82 ( 8 ) =  91.86
stand there and go up and down CRIT  S
Use S because it is the st dev of resid.
STAT +- CRIT (SE)
91.86 +_ Tcrit (7.7)
Tcrit is invt(.05, 73)

Question 27

For the following output for the association between test score and amount of time studied, what is the correlation coefficient?
OUTPUT: n=75 dep var: test score
VAR coeff se coeff t stat p
intercept 45.3 4.3 10.53 0.000
study time 5.82 2.66 2.189 0.0159
r-square: 77.5 S=7.7

Answer 27

if r squared is .775, then you have to take sqrt of that..

So r= 0.8803

Question 28

What is the common misconception about confidence intervals?

Answer 28

They know you stand at your stat and reach up and down.. BUT… People think that their statistic is in the middle of the pile of p hats or x bars!
in reality, they are almost definitely NOT!!
their statistic is most likely out on one of the sides, and they are reaching up and down and trying to catch the center!!! YOU ARE NOT IN THE MIDDLE OF THE PILE!!