The classic normal linear regression model assumptions are as follows: I. The relationship between the dependent variable, Y, and the independent variable, X, is linear. A linear relationship implies that the change in Y due to a one unit change…

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…

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…

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…

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…

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…

Measures of central tendency are values that tend to occur at the center of a well-ordered data set. As such, some analysts call them measures of central location. Mean, median, and mode are all measures of central tendency. Even then,…