Regression analysis in statistics is a predictive analysis concept that uses a linear model to describe the correlation between dependent and independent variables. There are two types of regression analysis based on the number of independent variables known as a predictor or exogenous or 'regressors.' Regression model with one predictor variable is a linear regression model. Regression analysis with two or more exogenous variables is known as multiple regression (Boston University, nd).
The linear regression model describes one variable as a function of another variable. The dependent variable, also known as an outcome, endogenous, criterion, variable, or 'regressand' is expressed as a function of the independent variable, and their relationship is as illustrated below; (Boston University, nd).
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≡ f( , ) +
The relationship regression model defines the relationship in the form of a regression equation and offers a strategy to compute coefficients for such relationships. Linear regression equation uses explanatory variables (independent variables) and has a general formula shown below (Fox, 2011).
Y = + +
Also denoted as Alpha (α) is a coefficient of y-intercept (when explanatory variable is Zero (x-axis))
Beta (β) represent coefficients for the independent variable in predicting Y.
= error term
Case Study: IMF Report the World Economic Outlook (WEO) October 2020
A report published by IMF in October 2020 shows economic growth projections for countries and different clusters based on development status. The report is accessible online through a link https://www.imf.org/-/media/Files/Publications/WEO/2020/October/English/text.ashx .
Q1; Significance of the report
The report is useful to the global community as it is useful in economic planning for countries. Although the recession caused by COVID19 leading to negative indexes to all in 2020, 2021 would record positive growth.
Q2. Using Y= f (X) +E notation, identify the independent and dependent variables.
Data provided on page "9" entitled "Table 1.1. Overview of the World Economic Outlook Projections" can be used to create multiple regression for the economic index for 2021 from indexes of 2019 and 2020.
| variables | 2019 | 2020 | 2021 projections |
| Advanced Economies | 1.7 | – 5.8 | 3.9 |
| United States | 2.2 | – 4.3 | 3.1 |
| Euro Area | 1.3 | – 8.3 | 5.2 |
| Germany | 0.6 | – 6.0 | 4.2 |
| France | 1.5 | – 9.8 | 6 |
| Italy | 0.3 | – 10.6 | 5.2 |
| Spain | 2 | – 12.8 | 7.2 |
| Japan | 0.7 | – 5.3 | 2.3 |
| United Kingdom | 1.5 | – 9.8 | 5.9 |
| Canada | 1.7 | – 7.1 | 5.2 |
| Other Advanced-Economies | 1.7 | – 3.8 | 3.6 |
The independent variables for the model would be growth indexes for 2019 and 2020
The dependent variable – 2021 projection
Q3. How might the research models presented be wrong?
Like any other model, IMF research doesn’t differ from those generated in 2019 for 2020, which produced a positive growth rate. The research models presented can be wrong because it does not consider uncertainties and consumer behavior that is unpredictable and changes depending on various factors. Regression relationship function has that denotes unknown parameters
What types of error might be present in the reported research?
In regression modeling, standard error expressed as multiple R should be reported
In regression analysis, R-squared indicates the degree to which the independent variable influences the dependent variable. R-squared is defined as a percentage, and therefore we can state the high the rate, the more significant the reliability of the model in predicting the dependent variable. If R-square is low, it signifies other factors that influence the outcome apart from the captured variable/s. Adjusted R square is controlled by two factors depending on the number of independent variables. Adjusted R square in regression model depends on Sample size (n) and the number of multiple regression variables. Statistically, the greater the sample size, the higher the credibility of statistical analysis results. An increase in sample size increases adjusted R square and increasing Independent variables increases errors (Fox, 2011).
Model results
|
Coefficients | ||||||||||||
| Intercept | 0.385546 | ||||||||||||
| xi | 0.597202 | ||||||||||||
| xii | -0.46031 | ||||||||||||
References
Boston University School of Public Health. (nd). The Power of Multiple Regression Models. Retrieved from; https://sphweb.bumc.bu.edu/otlt/MPH-Modules/PH717-QuantCore/PH717_MultipleVariableReg
Fox, J. (2011). Nonconstant Error Variance In Regression Diagnostic. Retrieved from: http://methods.sagepub.com/base/download/BookChapter/regression-diagnostics/n6.xml
International Monetary Fund. (2020). World Economic Outlook. Retrieved from: https://www.imf.org/-/media/Files/Publications/WEO/2020/October/English/text.ashx .
