Research Consultancy

16/02/2024

02/02/2023

𝐊𝐞𝐲 𝐀𝐬𝐬𝐮𝐦𝐩𝐭𝐢𝐨𝐧𝐬 𝐨𝐟 𝐎𝐋𝐒: 𝐄𝐜𝐨𝐧𝐨𝐦𝐞𝐭𝐫𝐢𝐜𝐬 𝐑𝐞𝐯𝐢𝐞𝐰

OLS (Ordinary Least Squares) is a popular statistical method used to estimate linear regression models. There are several assumptions that need to be met in order for OLS to produce reliable and accurate results.
The assumptions of Ordinary Least Squares (OLS) regression analysis include:

• Linearity: The relationship between the dependent and independent variables must be linear.

• Independence of errors: The errors are independent and have equal variances.

• Normality of errors: The errors follow a normal distribution.

• No multicollinearity: The independent variables are not highly correlated.

• No omitted variable bias: All relevant variables have been included in the model.

• No autocorrelation: The errors are not autocorrelated.

• Homoscedasticity: The variance of the errors is constant across all values of the independent variables.

If these assumptions are not met, the results of OLS regression analysis can be biased and unreliable. Here are some common violations of these assumptions and the remedies for each:

• Non-linearity of the relationship between the dependent and independent variables: This occurs when the relationship between the variables is not linear.
Remedy: Transform the variables or use a non-linear regression model.

• Heteroscedasticity: This occurs when the variance of the residuals is not constant across all observations. Remedy: Heteroscedastic errors can be corrected by transforming the dependent variable, using weighting schemes, or by using models such as weighted least squares or heteroscedasticity-consistent standard errors.

• Autocorrelation: This occurs when the residuals are correlated with each other.
Remedy: Use a time series model or a spatial regression model.

• Multicollinearity: This occurs when the independent variables are highly correlated with each other. Remedy: Remove one of the highly correlated variables or by combining the variables into a single composite variable.

• Non-normality of the residuals: This occurs when the residuals are not normally distributed.
Remedy: Non-normal errors can be transformed to a normal distribution using techniques such as the logarithmic or square root transformations.

• Omitted variable bias: Omitted variable occur when relevant variables have been excluded in the model. Remedy: Omitted variable bias can be corrected by including all relevant variables in the model.

• Outliers: This occurs when there are extreme values that can greatly affect the regression results.
Remedy: Remove the outliers or use robust regression techniques such as the Tukey method.

In summary, it is important to understand the assumptions of OLS and to check for their violations before conducting regression analysis. The remedies for each violation can help ensure that the results are accurate and reliable.

Compiled and Organized by: Abdalla Haji

02/02/2023

𝐋𝐢𝐧𝐞𝐚𝐫 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐌𝐨𝐝𝐞𝐥:

• Linear regression model is a statistical method that is used to examine the relationship between two continuous variables: independent variable (X) and dependent variable (Y).

• In this model, a linear equation is used to predict the value of Y based on the value of X.

• The goal of a linear regression model is to find the line of best fit that minimizes the distance between the actual values and the predicted values.

• The equation for a linear regression model is y = b0 + b1x, where b0 is the y-intercept and b1 is the slope of the line.

• Points in a linear regression model are used to plot the data and determine the line of best fit.

𝐋𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐌𝐨𝐝𝐞𝐥:

• A logistic regression model is a statistical method used to analyze the relationship between a binary dependent variable y and one or more independent variables (x).

• Unlike linear regression, logistic regression models are used to model the relationship between two binary outcomes.

• The goal of a logistic regression model is to determine the probability of a certain event occurring based on the values of the independent variables.

• The equation for a logistic regression model is P(y) = 1/(1 + e^(-b0 - b1x)), where b0 is the y-intercept and b1 is the slope of the line.

• Points in a logistic regression model are used to plot the data and determine the probability of a certain event occurring based on the values of the independent variables.

𝐌𝐮𝐥𝐭𝐢𝐩𝐥𝐞 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐌𝐨𝐝𝐞𝐥:

• A multiple regression model is a statistical method used to analyze the relationship between a dependent variable y and multiple independent variables (x).

• In this model, multiple regression equation is used to predict the value of Y based on the values of multiple X variables

• The goal of a multiple regression model is to determine the relationship between the dependent variable and each independent variable and to find the equation that minimizes the distance between the actual values and the predicted values.

• The equation for a multiple regression model is y = b0 + b1x1 + b2x2 + ... + bnxn, where b0 is the y-intercept, b1, b2, ..., bn are the slopes of the lines, and x1, x2, ..., xn are the independent variables.

• Points in a multiple regression model are used to plot the data and determine the relationship between the dependent variable and each independent variable.

Compiled & Organized by: Abdalla Haji