The Least Squares Criterion
The linear relation between the dependent and independent variables is described as follows: $$Y_i =\beta_0+\beta_1X_i+\epsilon_i,\ i=1,2,…,n$$ Where: \(Y\) = dependent variable. \(X\) = independent variable. \(\beta_0\) = intercept. \(\beta_1\) = slope coefficient. \(\epsilon\) = error term which is the observed…
Dependent and Independent Variables
Linear regression forecasts the value of a dependent variable given the value of an independent variable. It assumes that there is a linear relationship between dependent and independent variables. A dependent variable is predicted by an independent variable and is…
Analytical Duration and Empirical Duration
Differences between Analytical Duration and Empirical Duration Analytical duration refers to estimating duration and convexity using mathematical formulas (as done in the previous learning objectives). Analytical duration approximates the effect of changes in benchmark yields on bond prices by assuming…
Hypothesis Test Concerning the Equality of the Population Means
Analysts are often interested in establishing whether there exists a significant difference between the means of two different populations. For instance, they might want to know whether the average returns for two subsidiaries of a given company exhibit a significant…
Decision Rules in Hypothesis Tests
The decision rule refers to the procedure followed by analysts and researchers when determining whether to reject or not to reject a null hypothesis. We use the phrase “not to reject” because it is considered statistically incorrect to “accept” a…
Test Statistic, Type I and Type II Errors, Power of a Test, and Significance Levels
A test statistic is a standardized value computed from sample information when testing hypotheses. It compares the given data with what an analyst would expect under a null hypothesis. As such, it is a major determinant of the decision to…
