Econometrics is the quantitative measurement and that analyses the actual business and actual business and economic phenomena. It makes attempts to quantitatively bridge the gap between economic notion and the real world.
Uses of econometrics
It is used to quantify and measure marginal effects, while also estimating numbers for theoretic equations. Econometrics is used in testing the hypothesis around economic theory and strategy. It is used to forecast future economic activity using past data. Leaders are equipped on what decisions to make based on the extent to which econometrics can shed light on the future.
Purpose of a regression estimation.
It is used to assess how fit the estimated equation is when compared to the theoretical equation.
Meaning of estimated coefficients
Reason(s) for an ‘insignificant’ result for an estimated coefficient of the parameter
The insignificance is due to the estimated coefficient being greater than the common level of 0.05.
Reasons and conditions to use ‘2’ as a ballpark number for a critical ‘t’ value
The two-sided test is used to test whether an estimate coefficient is significantly altered than zero. It also test whether an expected coefficient is considerably different from a specified value.
Confidence interval, its calculation and reasons to calculate it
It is a range of values that are to comprise the true amount of beta a convinced percentage of the time.
Confidence interval = beta hat (+/-) t-statistic*standard deviation of the beta hat.
It tells how specific a coefficient estimate is.
P-value and its use in determining the reliability of the estimated coefficient
If the p-value is less than the level of significance and if beta hat(k) has the sign implied by the alternative hypothesis, reject the null hypothesis. If this is not met, not to reject the null hypothesis.
Example of displaying different uses of one-sided versus to sided t-Tests
One-sided t-tests (LaHuis et al., 2014). Null hypothesis: beta  is less than or equal to zero versus the alternative hypothesis: beta  is greater than zero.
Two-sided t-tests. Null hypothesis: beta  equals to zero vs. alternative hypothesis: beta  is not equal to zero.
Nature, role, and importance of F-test
It is designed to deal with a null hypothesis that contains both multiple and single predictions about a group of coefficients (Zietz et al., 2008). F-test tests the significance of seasonal dummies, testing the hypothesis of significant seasonality in the given data.
Revenue = 1550 -0.556*rent -100
Revenue is the dependent variable, it depends on the other variables.
1550 is the intercept on the y-axis,
-0.556 is the coefficient of rent.
Rent is the explanatory variable, its one unit change causes a one unit change in revenue,
-100 is the error term, and it is independent of both revenue and rent.
The technique is mostly used to obtain estimates since it is reasonably easy to use. It calculates beta hats by minimizing the sum of the squared residuals (Zietz et al., 2008). The method is a mathematical technique that produces an estimate of the real regression coefficient of a population after its application. The beta has been produced by the process are estimates where it selects the beta hats that minimize the squared residuals summed over the total sample data points. R-squared is then used to measure the fit
explain possible uses of unexplained error terms in the OLS.
Collecting data that is required when quantifying the models.
The linearity of the equation form. That is if the line produced is straight.
The slope coefficient should have a linear effect on the overall equation; hence the equation must be linear.
The researcher might omit some important values from the equation. This omission produces variations in the dependent variable. He might also make errors when measuring the dependent variable, thus producing a change in the overall linear model (LaHuis et al., 2014). Creating a different functional form other than the correct theoretical equation. Researchers might do or add an unpredictable action which alters the given model.
Regression is used to quantify the relationships between one variable and other variables. It identifies the closeness and how well the determined relationship is.
An omission of an important independent variable correlated with the inclusion of an independent variable.
An assumption that a low level of significance is better. However if the level of relevance is low, the probability of Type II Error increases.
There is no perfect linear function of the explanatory variable to other explanatory variables.
The interpretations of the error terms are uncorrelated with each other.
The error term is normally distributed. However, estimating OLS does not require normality assumption helping in hypothesis and confidence intervals.
(i) State the hypothesis to be tested. It is before the estimation of the equation. Break the hypothesis into two theories. That is the null hypothesis and alternative hypothesis.
(ii) Perform a two-tailed test, to test the alternative hypothesis with values on both sides of the null hypothesis.
(iii) Use a typical technique to hypothesize an expected value for every coefficient then determine whether to reject the null hypothesis. Two errors might occur; if type 1 occurs, reject the null hypothesis if type 2 occurs do not deny the null hypothesis. Alternatively, one can use the decision rule method to decide if to reject the null hypothesis. It is a comparison of a sample statistic with a critical value. Then a division of the range of possible value of beta hats is made into row regions; acceptance and rejection region.
The t-Test. It is used to test hypotheses about individual slope coefficients
The confidence interval. It is a range of values at a certain percentage of time containing the real amount of beta. They are vital in telling the preciseness of a coefficient estimate.
The F-test has a design of handling a null hypothesis containing multiple hypotheses or a single hypothesis around a collection of coefficients. One translates the null hypothesis into constraints placed on the equation. Then an estimation of the constrained equation with OLS is done. After the estimation, there is a comparison of the fit of the constrained equation with the fit of the unconstrained equation (LaHuis, 2014). “The decision rule is rejection of the null hypothesis if calculated F-value is more significant than the critical F-value.”
These errors can be reduced by using the 5-percent level of significance.
A t-test is used in testing the hypothesis about individual slope coefficients. It stands as the most suitable test whenever the random error term has a normal distribution. And then an estimation of the variance made. The t-values for every estimated coefficient of standard multiple regression equation are calculated (Cameron and Trivedi, 2013). The mostly used t-statistic is used to test whether a particular regression coefficient is significantly different from zero in most regression hypotheses. The calculated t-value and the critical t-value comparison, form the basis on which we reject or not reject the null hypothesis.
Using the t-test for testing the entire population, whereas it is used to make inference about the real value of a parameter from a sample of the whole population.
One translates the null hypothesis to constraints that are afterward attached on the linear equation. Make an estimate of the constrained equation with OLS and then a compare the fit restricted equation with the fit of the unconstrained equation.
Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data (Vol. 53). Cambridge university press.
LaHuis, D. M., Hartman, M. J., Hakoyama, S., & Clark, P. C. (2014). Explained variance measures for multilevel models. Organizational Research Methods, 17(4), 433-451.
Osborne, J. W. (2014). Best practices in logistic regression. Sage Publications.
Zietz, J., Zietz, E. N., & Sirmans, G. S. (2008). Determinants of house prices: a quantile regression approach. The Journal of Real Estate Finance and Economics, 37(4), 317-333.