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| What are the assumptions of the classical linear regression model? |
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Definition
(most assumptions pertain to the error term (residual term))
- Linear relationship between the dependent and the independent variable.
- Independent variable is uncorrelated with the error terms.
- Expected value of the error term is 0.
- The variance of the error term is constant for all Xi
- No serial correlation of the error term (knowing the value of an error for one observation does not reveal information concerning the value of an error for another observation.
- The model is correctly specified in that it includes only the appropriate independent variables and does not omit variables.
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Term
What does homoskedasticity refer to?
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Definition
| refers to the condition that the variance of the error term is constant for all Xi |
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Term
Heteroskedasticity means...
Conditional heteroskedasticity means... |
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Definition
the variance of the error terms varies over the sample.
the variance is a function of the independent variables.
(learn the formulas on page 245 of book 1) |
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Term
| What does the gauss-markov theorem state? |
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Definition
Gauss-Markov steorem says that if the classical inear regression model assumptions are true, then the OLS estimators have the following properties:
- The OLS estimated coefficients have the minimum variance
- The OLS estimated coefficients are based on linear functions
- The OLS estimated coefficients are unbiased, which means that in repeaetd sampling the averages of the coefficeients from the sample will be distributed around the true population parameters
- The OLS estimate of the variance of the errors is unbiased.
(BLUE)
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Definition
| CLT says when taking samples from a population, if the sample size is large then the sums of the independent and identically distributed random varialbes and the means of the individual samples will be normally distributed. |
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Term
| What is the coefficient of determination (R2) ? |
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Definition
| It's a measure of the goodness of fit of the regression. It's interpreted as teh % of variation in the dependent variable explained by the independent variable. |
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Term
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Definition
TSS = ESS + RSS (total sum of squares = explained sum of squares + residual sum of squares)
R2 = ESS / TSS
R2 = 1 - (RSS / TSS) |
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Term
| Describe the Jarque-Bera test and give the formula for it: |
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Definition
The Jarque-Bera test is a method for testing if the normaility assumption is reasonable.
It assumes normality and rejects the hypothesis if the statistic is too large.
The formula for the statistic is:
JB = n/6 x [S2 + (K-3)2/4]
where:
n = number of observations
K = kurtosis
S = skewness |
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| When is the JB test appropriate? |
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Definition
| for large samples (n>30, preferably n>100) |
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Term
| What is the result of a JB test intrepreted as? |
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Definition
| a chi-square distribtuion with 2 df |
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Term
| What does the standard error of a coefficient indicate? |
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Definition
the standard error of a coefficient indicates the accuracy of the estimated OLS coefficient with respect to its population parameter.
Each standard error is the square root of the variance of the corresponding coefficient. |
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Term
If the value for variance is not known, it is estimated and replaced in the equation with an estimate from the sample:
give the equation: |
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Definition
= sumei2 / (n-2)
= sum (Yi - Mean Y)2 / n-2 |
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Term
| In hypothosis testing an OLS model, how do you compute z and t (short formulas) |
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Definition
z = b1 - B1 / se(b1)
If population variance is not known, need to use sample variance, and then the t-distribution rather than the z distribution. t is calculated as:
t = b1 - B1 / se(b1)... the researcher will compute the t statistic by replacing B1 which is not known, with the hypothesised value denoted B1,H0 |
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| In a simple two-variable regression, the square root of R2 is the correlation coefficient (r) between Xi and Yi. If the relationship is positivbe then R = square root (R2) |
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Definition
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Term
| How is the correlation coefficient different from the coefficient of determination? |
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Definition
correlation coefficient indicates the sign of the relationship, coefficient of determiantion does not.
Secondly, coefficient of determination can apply to an equation with several independent variables and it implies causation. Correlation coefficient only applies to two variables and does not imply causation. |
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