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For each of the following statements determine if it is True or False. In case of a False statement, provide the correction to make it True.
For each of the following statements determine if it is True or False. In case of a False statement, provide the correction to make it True.1. e is called the stochastic error term, and ε is called the residual term.2. ε has a value that is random but cannot be observed.3. ε is the difference between the dependent variable and the estimated value of thedependent variable.4. β^1 has just one unique value.5. β1 has just one unique value.6. The value of β1 can be fully determined using the values of the dependent andindependent variables in the sample.7. β1 represents the amount of change in the independent variable when the dependentvariable is increased by 1 unit, holding other things unchanged.8. The only time εi is zero is when an observation is located on the true regression line.9. In a simple linear regression on a sample of size N, we have N different residuals.10. β0 is the value of the dependent variable when all independent variables are set at zerovalue.11. β^1 in a sample of size N, has N different values.12. Yi^=β^0 +β^1 Xi+ei13. Yi=β^0 +β^1 Xi+εi14. E(Yi| Xi )=β0 +β1 Xi is a called the population (true) regression line.15. The estimated regression line is a unique line.16. The population regression line is a unique line.17. Y^ is called the predicted value of the dependent variable.18. The residual e can be positive, negative or zero depending on the observation it iscalculated from.19. TSS can be positive, negative or zero depending on the sample it is calculated from.20. ESS is a measure for the total changes (variation) in the estimated part of Y21. TSS is a measure for the total changes (variation) in the independent variable.22. Y^ cannot be larger than the true value of the dependent variable.23. If Y^ is smaller than the dependent variable for an observation, the residual for thatobservation will be negative.24. If we add RSS and TSS , we’ll get the ESS.25. The true value of Y is not observable.
