Economic Statistics Class Notes 4/27/09
14. Lagged Dependent Variable (a different model structure) Use past values of the dependent variable to predict the current value Original Model:
WARNING:
VALID
If the model has autocorrelation, the Durb
Economic Statistics Class Notes 4/24/09
11. An F Test on a Subset of Variables Purpose To evaluate the impact of a subset of independent variables on the multiple regression model The two models are naturally related Effects of excluded variables
Economic Statistics Class Notes 4/22/09
Q: How can we tell if the addition of new explanatory variables really improves the model. Model = a model of supply and demand for eggs Income affects demand, so you have to have a model for income as well
Economic Statistics Class Notes 4/20/09
6 different variables Count the columns correctly to get the correct dependent variable. The data in the economic report are nominal data you need REAL data thats why you need the CPI data Everyone will use
Economic Statistics Class Notes 4/17/09
c.) Autocorrelation A situation in which error terms are linearly related to one another * There is a relationship between the error terms; they are supposed to be totally random If there is a relationship
Economic Statistics Class Notes 4/15/09
9.) b.) Heteroskedasticity different spread = a situation in which the variance of errors (the true variance of errors from our population model ) is not constant
1. Effect: OLS (Ordinary Least Squares) est
Economic Statistics Class Notes 4/13/09
Recall Multicollinearity Two or more independent variables are linearly related
Estimators: 1.) Should be unbiased 2.) Should be efficient Multicollinearity does not affect bias or efficiency of our estim
Economic Statistics Class Notes 4/10/09
Recall: Multiple Regression Model 7. Measures of Fit It is still true that: o SST = SSE + SSR o SST = Total Sum of Squares
Economic Statistics Class Notes 4/8/09
I. The Multiple Regression Model a. The population model
b. The sample model
c. Estimation procedure
d. Assumptions of the Model In 3-D space, a plane is a surface For 3-D space, replace the word LINE with
Economic Statistics Class Notes 4/6/09
EXAM #3 Material
Economic Report of the President: Downloadable Reports Download Entire Reports NO Statistical Tables YES Go ahead and choose 2009 For our purposes, we are interested in: Copy Gross Domesti
Economic Statistics Class Notes 4/1/09
Dummy Variables
Two kinds: o Intercept dummy variable o Slope dummy variable Leads to an X% change in
More on Dummy Variables: The slope dummy variable use to evaluate the effect of a qualitative charact
Economic Statistics Class Notes 3/30/09
Inverse relationship between distance and exports, so the alternative hypothesis is H1: B < 0 For exam Proofs: Properties of regression line Sum of the errors = 0 Correlation coefficient * (Sy / Sx) proofs k
Economic Statistics Class Notes 3/27/09
2. The Standard Error of the Estimate:
Recall: The sample variance of y This is a measure of the average of the squared deviations of y from its mean
Note that:
In general, we want the standard deviatio
Economic Statistics Class Notes 3/25/09
We can draw a line to fit any set of data, but the question is, is that line a good fit? RECALL:
There is a gap between the actual value of Y and the predicted value of Y. Yi = actual Y value when X = Xi Yi
Economic Statistics Class Notes 3/23/09
Recall:
Estimators: a and b and thus there are (n 2) degrees of freedom. The number of degrees of freedom depends on the number of estimators (CHECK THIS):
Recall A Confidence Interval for
with
unknown
Economic Statistics Class Notes 3/11/09
Recall Regression Analysis Problem Find the line that fits best
Problem How to estimate a & b Solution choose a and b so that the sum of the squared residuals is minimized:
BE SURE TO KNOW WHAT HE IS S
Economic Statistics Class Notes 3/11/09
Do the representative questions for the quiz on Wednesday: 10.11 pp. 348 10.12 pp. 348 10.16 pp. 351 Do a t test but use the Z-table to find the p-value 10.21 pp. 351 11.21 pp. 388 11.27 pp. 393 (f-sta
Economic Statistics Class Notes 3/6/09
HYPOTHESIS TESTING
Case #3: A Test on an Assumed Value of the Variance
Suitable Test Statistic: 1. Known Distribution necessary, not sufficient because it also has to apply to the problem
Null hypothesis a
Economic Statistics Class Notes 3/4/09
Case #2 A test population mean when the variance is NOT KNOWN: Step 1: H0: u = 30
If H0 is true, (Xbar u0) will be approximately zero. This is how we are enabling a comparison between the hypothesis and t
Economics Statistics Class Notes 3/2/09
NO MORE PROOFS Application of concepts now
Hypothesis Testing
Case 1 A Test on the Population Mean (u) with Standard Deviation (o) known 1. An appropriate null and alternative hypothesis Ho: u = u0 = 10 H1
Economic Statistics Class Notes 2/25/09
Q: How do we know when to use Z vs. t vs. chi-square vs. F Short answer to use t, Chisquare, or F, the parent population must be distributed normally. Chisquare is either a square of standard normal variable
Economic Statistics Class Notes 2/23/09
HOMEWORK PROBLEMS: 8.13 pp. 288 8.16 pp. 289 8.27 pp. 294 9.27 pp. 321 9.29 pp. 321 These problems represent each problem type!
For confidence intervals, you need to find a Z value for both sides of
Economic Statistics Class Notes 2/20/09
Confidence Intervals
Case I A Confidence Interval for the population mean when the (variance/standard deviation) is KNOWN We are going to use Xbar because it is unbiased and consistent. o The probability th
Economic Statistics Class Notes 2/18/09
Exam #1 Page numbers for this material in the textbook Recognize the formula for the estimator t-distribution: Z, t, f, and chi-square distributions
We were able to take a form that we did NOT recognize
Economic Statistics Class Notes 2/16/09
Study Guide Wednesday Will have a list of all the proofs you need to memorize EXAM 2/27/09 The exam will be almost entirely proofs DONT memorize the steps, MEMORIZE the procedure! If there is a square,
Economic Statistics Class Notes 2/13/09
What we would like to have for our estimator:
D. The Properties of S^2 (sample variance) as an estimator of true POPULATION VARIANCE
PROOF:
Step 1: Rework Shat^2 formula
Economic Statistics Class Notes 2/11/09
Properties of Xbar o Estimator Take a random (representative) sample Get an estimate of the population
The expected value of Xbar is equal to the population mean.
Recall:
1. The distribution of Xbar is
Economic Statistics 2 Class Notes 2/9/09
X
QUESTION: What do we see? ANSWER: The mean of all sample mean values (Xbar) equals the mean of the random variable X (the population mean, ) the population parameter we want to estimate. Also, the sampli
Economic Statistics Class Notes 2/6/09
NEW TOPIC: II. Estimation of Population Parameters A. Definitions: a. Estimator A random variable used to estimate a population parameter i. Also known as a sample statistic (a statistic is a characteristic o