Quantitative Methods
Data Presentation as a Histogram or a Frequency Polygon
Histogram A histogram shows the distribution of numerical data in the form of a graph. However, it is very similar to a bar chart, a histogram groups data into intervals. To construct a histogram, you need to establish all the…
Tests of Independence Using Contingency Table Data
With categorical or discrete data, correlation is not suitable for assessing relationships between variables. Instead, we use a non-parametric test called the chi-square test of independence, which employs a chi-square distributed test statistic. We employ a contingency table to structure…
Tests of Independence
Parametric versus Non-parametric Tests of Independence A parametric test is a hypothesis test concerning a population parameter used when the data has specific distribution assumptions. If these assumptions are not met, non-parametric tests are used. In summary, researchers use non-parametric…
Functional Forms for Simple Linear Regression
To address non-linear relationships, we employ various functional forms to potentially convert the data for linear regression. Here are three commonly used log transformation functional forms: Log-lin model: In this log transformation, the dependent variable is logarithmic, while the independent…
Predicted Value and Prediction Interval 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: $$\hat{Y}=\hat{b}_0+\hat{b}_1X$$ 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),…
Measures of Fit and Hypothesis Tests of Regression Coefficients
The sum of Squares Total (SST) and Its Components The 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…
Assumptions Underlying Linear Regression
Assume that we have samples of size \(n\) for dependent variable \(Y\) and independent variable \(X\). We wish to estimate the simple regression of \(Y\) and \(X\). The classic normal linear regression model assumptions are as follows: Linearity: A linear…
Introduction to Linear Regression
Linear regression is a mathematical method used for analyzing how the variation in one variable can explain the variation in another variable. Let \(Y\) be the variable we wish to explain. As such, the observation of this variable is \(Y_i\),…
Applications of Big Data and Data Science
Data science is an interdisciplinary field that uses developments in computer science, statistics, and other fields to extract information from Big Data or data in general. Data Processing Methods Data analysts and scientists in big data analysis use different data…
