Exam 2 Cumulative Review

Question 1

dependent variable

Answer 1

-the variable that is dependent on the independent variable, what is being measured
-y-variable
-left hand/left side variable
regressand

Question 2

independent variable

Answer 2

-the variable that affects the dependent variable
-right hand variable
right side variable
-regressor

Question 3

7 steps for calculating predictor x in regression equation

Answer 3

1. calculate E(X) and E(Y)
2. calculate “actual minus expected” for each variable, for each observation
3. square “actual minus expected” JUST FOR X
4. DO NOT square “actual minus expected” for Y
5. instead, take (actual - expected of X) x (actually - expected for Y)
6. add up what you got for 3 and 5
7. take the ratio of the two (with XY on the top)

Question 4

calculating intercept for regression equation

Answer 4

take the slope you calculating…

1. multiply it by your E(x)
2. subract that from your E(y)

Question 5

how to interpret regression equation (use following example):
Y = 1.28 + .10443X

Answer 5

when the value of our X variable increases by 1, the value of our Y variable increases by .104

for every $10 increase in hourly income, the number of meals eaten out in a month increases by about 1

Question 6

residual of a regression

Answer 6

the difference between the predicted Y and the actual Y according to the data

Question 7

total sum of squares

Answer 7

the actual variation in Y (dependent variable)

Question 8

explained sum of squares

Answer 8

the modeled variation in Y (dependent variable)

Question 9

R^2

Answer 9

ratio of ESS/TSS

-used to tell how much of variance an IV explains in the DV

Question 10

7 steps to calculating R^2

Answer 10

1. take the actual values of Y, get E(y)
2. take (act - exp)Y; square it, add it up
3. that’s the actual variation in Y
4. you have already run the regression
5. use the results to calculated predicted values of Y for every X
6. take (Predicted - Expected)Y; square it; add it up
7. take the ratio of #6 over #3

Question 11

classic linear regression model assumptions

Answer 11

1. the model is linear in its parameters and has an additive error term
2. the values for the IV’s are derived from a random sample of thepopulation and contain variability
3. no IV is a perfect linear function of any other IV (no perfect colinearity)
4. the error term has expected value of zero
5. the error term has a constant variance (homoskedasity)

Question 12

if the error term has an expected value of zero and also has a constant variance…we can conclude what about the error term? and then what about the estimate for b-hat?

Answer 12

1. error term has a normal distribution
2. our estimate B-hat is a linear function of the error term
3. therefore, B-hat is normally distributed
4. this means we can test our individual estimators for significance

Question 13

equation for testing (tstat) individual estimator’s significance (assuming homoskedasticity)

Answer 13

(Betahat - 0) / standard error of Betahat

it is minus zero because that is our expected value for beta-hat

Question 14

what does having a t-stat of 1.96 exactly mean for our beta-hats?

Answer 14

this means I could create an interval of a certain width (1.96 standard errors above and below our hypothesized mean) and if I repeated by sampling 100 times, 95 out of the 100 times that interval would contain the true population mean
-so if the interval for betahats on the printout from SAS contained zero, we cannot reject the null (beta = 0)

Question 15

if our r^2 and SER isn’t great, what else can we check to find significance in our regression model?

Answer 15

we can check the t-stats for each individual beta-hat…we can’t conclude they are key drivers, but it does indicate and real and positive relationship

Question 16

what is the standard error of beta hat?

Answer 16

-it is the standard deviation of the sampling distribution…it measures the spread

remember that beta hat is a random variable, therefore it has an expected value and a distribution
-that distribution has a spread, measured by the variance and the SD

Question 17

homoskedastic

Answer 17

variance of the error term is constant

Question 18

heteroskedastic

Answer 18

variance of the error term changes

Question 19

the smaller the standard error of our beta hat, the larger our t-stat. AND the larger our t-stat, the more likely we will reject the hypothesis that b = 0…why?

Answer 19

when our standard error gets small, this means the distribution is getting less and less wide

• if our distribution of beta hat is very tight, our distribution is not very spread out
• this means there’s less and less of a chance that values will vary much from our expected value…which means there is less of a chance that zero will be in that interval

Question 20

f-statistic

Answer 20

used to test a joint hypothesis

• the hypothesis that ALL of our betas are really zero
• B1=0 AND B2=0, not B1=0 OR B2=0

Question 21

formula for f-stat

Answer 21

(R^2 / k ) /
((1-R^2) / (n-k-1))

k is number of IV’s
n is number of observations

Question 22

formula for finding t-stat of restricted and unrestricted variables

Answer 22

((RSSrestricted - RSSunrestricted)/ q ) /

(RSSunrestricted) / n-k-1 )

Question 23

explained sum of squares (regression sum of squares)

Answer 23

sum of squares of the deviations of the predicted values from the mean value of a response variable, in a standard regression model

Question 24

Standard error of observations

Answer 24

the Standard deviation of the error

-large values imply that actual values are a long away from our fitted line

Question 25

p-value

Answer 25

the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true

Question 26

binary variable

Answer 26

either/or situation to represent discrete variables

-in STATA, you identify one outcome as 1 and the other as 0