Flashcards
Regression and Hypothesis Testing: OLS, R², Errors
Cards in this deck (29)
- 1The error term in a regression equation is said to exhibit homoskedasticity if...it has the same variance of the explanatory variable
- 2Consider the following regression equation y = b1 +b12x1 +b2x2 + u. What does b1 imply?b1 measures the ceteris paribus effect of x1 on y.
- 3Which of the following is true of R²?R² shows what percentage of the total variationn in the dependent variable, Y, is explained by the explanatory variables.
- 4If an Independent variable in a multiple linear regression model is an exact linear combination of other independent variables.....the model suffers from the problem of perfect collinearity.
- 5The normality assumption implies that....the population error u is independent of the explantory variables and is normally distributed with mean zero an variance o².
- 6Consider the quation, Y=b1 + b2x2 + u. A null hypothesis, H0: b2 = 0 states that:X2 has no effect on the expected value of Y. The significance level of a test is the probability of rejecting the null hypothesis when it is true.
- 7Which oft he following tools is used to test multiple linear restriciton?F-test
- 8If by an unbiased estimator of by is consistent , then the...distribution of b1 becomes more and more tightly distributed around b1 as the sample size grows.
- 9In the following equoation gdp refers to gross domestic product, and fdi refers to foreign direct investments. LOG(gdp) = 2,65 + 0,527 log (bankcredit) + 0,222 FDI. Which of the following statements is then true?If bank credit increases by 1%, gdp increases b 0,527 %, the level of FDI remaining constant.
- 109 steps of Hypothesis Testing1. research hypothesis
2. null hypothesis
3. level of significance
4. Method of statistical analysis
5. test of significance
6. degrees of freedom
7. assumptions
8. decision
9. conclusion - 11What is BLUE ?1. Model is linear
2. Variation in the sample
3. expected value term zero
4. disturbance term is homoskedastic
5. the values of the disturbance term have independent distributions
With assumptions through 1 to 5, we say that OLS coefficients are BLUE. Best Linear Unbiased Estimators. They are best, because they have the smallest variance across all unbiased estimators. Following the Gauss Markov theorem. If an estimator is unbiased, the distribution of the coefficient becomes more and more tightly distributed ariond the coefficient, as the sample size grows. - 12What is OLS?In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model, with the goal of minimizing the sum of the squares of the differences between the observed responses (values of the variable being predicted) in the given dataset and those predicted by a linear function of a set of explanatory variables. The least squares regression line minimizes the sum of the squared residuals.
- 13List Criteria for science characteristics of scienceCriteria: Rational, empirical, pragmatical. Characteristics: self-corrected, repeatable, scepticism. Science is the human attempt to provide the most parsimonious logical organization for the statements of fact on which there is common agreement. Parsimonious means to explain the most with the least, efficient. Where is the difference between variance and deviation? Whereas the mean is simply the average of all data points, the variance measures the average degree to which each point differs from the mean. (Calculation of variance uses squares because
- 14What does the significance level tell us?The significance level of a test is the probability to committing a type 1 error, rejecting H0 when you shouldn't. In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone. But if the p-value of an observed effect is less than the significance level, one may conclude that the effect reflect the parameters of the whole population, thereby rejecting the null hypothesis.
- 15Define error type IError I means to reject H0 when it's true. The probability of making such an error is alpha, which is the level of significance for a hypothesis test. An alpha level of 0,065 (5%) indicates that there is a 5% chance to reject the H0 when its true. To lower the probability/ risk of error type I, one can lower the level of alpha. But the lower the value, the less likely it is to detect a difference if one exists. (Example: A researcher finds that there is a difference between medications, when in fact it is not. )
- 16Define error type IIThe H0 Hypothesis is false but failed to reject the H0. This often happens when the sample sizes is too small. (Example: There is a difference between medication, but the researchers fail to detect it and accept H0)
- 17How is R2 to be interpreted?If we have a value of Rsquared, e.g. 0,6691, we can interpret 66,91 % of the variance in the dependent or observed variable can be explained or accounted for by the independent variables in the model. If the model tested by the F-Test is significant. Rsquared does not equal zero and one can conclude that there is a correlation.
At an alpha level of 5%: A correlation of xx% or greater could have been obtained 5 out of 100 times by chance/ sampling and 95 out of 100 times it the true coefficient in the population at this particular time. - 18Why are dummy variables helpful? Where are the risks?Dumm variables are. useful because they enable us. tp use. on single regression equotation to represent multiple groups. One has to leave the benchmark-group out because otherwise the model suffers of the "dummy variable trap", and a exact linear relationship among the variables in the regression equotation. This is as well known as multicollinearity, when two or more variables are highly correlated.
- 19What does the simple correlation measure ?The simple correlation coefficient measures the strength an direction of the linear relationship between the dependent and the independent variable. If there is a highly positive correlation, a straight line goes up to the right, a highly negative correlation shows a straight line down the right, a small positive correlation shows in loosely circled values around a slightly upping line and so on.
- 20What is Multicollinearity?Multicollinearity is, when independent variables are highly correlated. Multicollinearity is a problem because it can increase the variance of the coefficient estimates and make the estimators very sensitive to minor changes in the model. The result is that the coefficient estimates are unstable and difficult to interpret.
- 21List the assumption of a multiple regression model1. linear relationship between dependent and independent variable. The model is linear and correctly specified.
2. There is no exact linear relationship among the regressors (independent variables) in the sample. (Otherwise: multicollinearity) (We need at least two independent variables.)
3. The disturbance term is expectation zero. E(ui)=0 for all I (zero mean value)
4. The disturbance term is homoskedastic. 02ui = 02u for all I ( The deviation of the error term is constant and independent.
5. The values of the disturbance term have independent distribution
6. The distribution term has a. normal distribution. The population error u is independent of the explanatory variable, normally distributed with a mean zero variance o2 - 22Explain Homoskedasticity and HeteroskedasticityHomoskedasticity means that deviation of the error term is constant and. not dependent on the independent variable X. Heteroskedasticity means that the deviation of the error term is not constant and dependent on the independent variable.
- 23How can we test for Heteroskedasticity?White test of Breusch Pagan Test.
The white test adds the squares and cross products of all the independent variables to the equotation.
Using the Breusch Pagan Test:
1. Running the regression: y = ß0 + ß1xy + ß2x2 + ßnXn + €
2. Saving the residuals, E (errors) in E = Y - ^y
3. Square the Errors = E2
4. Run the regression E2 = ß0 + ß1xy+ß2x2+ßnXn + €
5. Research Hypothesis. H0 = ß0 = ß1 = ß2= ß2 = 0 (Testing for Homoskedasticity)
6. Using the F Test
7. If the p-value (Chi-square) is below 0,05, this indicates to reject the null hypothesis of homoscedasticity. --> Hetereoskedasticity - 24The range of the covariance is-unendlich <= Cov <= +unendlich
- 25In a data set, if two variables x and y have an extremely weak correlation, the a scatterplot of their values would fit loosely around .....a circle.
- 26When the variance o2, of the error variable e is a constant no matter what the value of x is, this condition is called...homoscedasticity
- 27What occurs when independent variable in your analysis are highly correlated=Multicolinearity
- 28What measures only the direction of the linear relationship between the dependent and the independent variable?Correlations Coefficient
- 29remember the t-observed = ß1 / s.e Develop a framework for hypothesis testing. Please fill each one of the steps and make a statistical decision wether you would reject or fail to reject the null hypothesis.1. research hypothesis:
2. Null hypothesis
3. Level of significance
4. Statistical Method
5. Test of Significance
6. Degrees of Freedom
7. Assumptions
8. Decision
9. Conclusion
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- MBA Flashcards on Untitled, created by Maximilian Becker on 27/02/2021.
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