Data Visualization
Data visualization refers to the presentation of data in a pictorial or graphical format using different graphs such as histograms, polygons, line charts, bar charts, etc. Histogram A histogram is a graphical representation of the data contained in a frequency…
Contingency Tables
A contingency table is a tabular representation of category-based data. It shows the frequencies for particular combinations of values for two discrete random variables, say X and Y. Each cell in the table represents a mutually exclusive combination of X-Y…
Data Organization for Quantitative Analysis
Typically, raw data can be organized into the following two formats for quantitative analysis: One-dimensional array: A one-dimensional array is the simplest format for representing a single variable, such as the daily trading volume of the stock exchange. Two-dimensional rectangular…
Using Timelines in Modeling and Solving Time Value of Money Problems
A timeline is a physical illustration of the amounts and timing of cashflows associated with an investment project. For cashflows that are regular and of equal amounts, the standard annuity formula or the financial calculator can be used. However, for…
Present Values, Future Values, Annuities, and Series of Unequal Cashflows
Future Values The Future Value (FV) of a Single Sum of Cash Flow The Future Value (FV) of a single sum of money is the amount that money invested today at a given interest rate (r) for a specified period…
Functional Forms for Simple Linear Regression
For non-linear relationships, we can use several functional forms to potentially transform the data to be used in linear regression. The following are the three often-used log transformation functional forms: Log-lin model: In this log transformation, the dependent variable is…
Predicted Value of a Dependent Variable
We calculate the predicted value of the dependent variable, \(Y\), by inserting the estimated value of the independent variable, \(X\), into the regression equation. The predicted value of the dependent variable, \(Y\), is determined using the following formula: $$\hat{Y}=\widehat{b}_0+\widehat{b}_1X$$ Where:…
Analysis of Variance (ANOVA)
The sum of squares of a regression model is usually represented in the Analysis of Variance (ANOVA) table. The ANOVA table contains the sum of squares (SST, SSE, and SSR), the degrees of freedom, the mean squares (MSR and MSE),…
Coefficient of Determination and F-statistic
Sum of Squares Total (SST) and Its Components Sum of Squares Total (total variation) is a measure of the total variation of the dependent variable. It is the sum of the squared differences of the actual y-value and mean of…
