Bivariate regression
Regression analysis is a very important tool of business research. Normally, the process of regression analysis starts with the determination of the variables. There are two types of variables, the dependent and the independent ( Cohen, Cohen, West & Aiken, 2013) . The bivariate regression analysis normally takes the form y = a + bx. In this case, y is the dependent variable while x stands for the independent variable. The independent variable is the one that influences changes in the dependent variable. It is vital to note that the independent variable is always fixed, whereas the dependent variable is flexible and varies depending on the fixed amount of the independent variable.
The intercept of a regression, which is normally labeled the constant, gives the expected mean value of the dependent variable when the independent variable is zero. For example, the intercept value in the regression function, y = a + bx, is a. It tells the expected value of y when x is at zero.
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It must be noted that the slope of a regression gives the rate of change in the dependent variable with respect to the changes in the independent variable. For instance, in the above linear regression function, the slope value b represents the amount of change in the dependent variable y, given a unit change in the independent variable x.
Regression analysis is very important for businesses, especially when it comes to research and development. It is important to note that businesses usually accumulate various forms of data. These data include the sales performance, profitability changes, information regarding the tastes and preferences of customers, market trends and the financial performance at the industry level. Using the regression analysis method to evaluate and draw useful meanings from the collected data helps businesses to make improved business decisions. Regression may be used in businesses to analyze the existing trends and make logical forecasts about the future. For instance, if the sales of a given company have been on the rise for the past few years in a row, a linear regression analysis of the monthly sales performance over these years under study would give an upward sloping graph line. Such a line depicts an upward trend in the sales performance of the company. This graph may be used to predict that the future of the company will experience a steady rise in its sales revenue.
Regression analysis is very effective in the evaluation of the price changes in the market. Linear regression helps businesses to analyze the impact of pricing on the behavior of consumers. For example, if a company alters its price level on specific commodities many times, it may take note of the resultant quantity of goods sold at each price level. Thereafter, the recorded data may be used to carry out linear regression with the total quantity sold as the dependent variable and price level as the independent variable. The produced graph line would show the trend in the decline of the quantity demanded by the customers in the market for every price increase. This graph may be used to inform and guide the future pricing decisions by the business management.
Linear regression is also very important in the assessment of business risk. For example, a health insurance firm may do a linear regression of the number of claims by each customer against age. This regression analysis would enable this company to realize that the older clients tend to present more health insurance claims than the younger ones.
Bivariate regression may be suitable for analyzing the relationship between the demand for monetary loans and the level of interest rates within the financial market of a specific country like the United States of America. In this case, the independent variable would be the interest rate level. The dependent variable would be the demand for the monetary loans by borrowers in the financial market.
The major types of regression analysis
There are two types of regression analysis, which include the simple and multiple regressions. The major similarity between simple and multiple regression analysis is the fact that they both have one dependent variable. The difference between these two types of regression is that multiple regression analysis is made up of more than one independent variable while the simple regression is comprised of just a single independent variable.
Some of the ways used to identify the independent variables for multiple regression analysis include the use of the P-values to determine the importance of a given variable. Statistical measures may also be used to establish the significance of each variable. In this case, the focus is usually on the coefficients of the variables.
The forward selection is a technique of model choosing, which starts without any variables. The F statistics is then calculated for every independent variable to determine its contribution to the model if a decision to include it is made. The p -values for these F statistics are then analyzed with respect to the SLENTRY= value, which is usually specified within the model statement (Harrell, 2015). The backward elimination technique is unique in the sense that the F statistics for a model including all independent variables is calculated. Variables are then eliminated from the model one at a time up to the point the new model achieves F statistics significant at the SLSTAY= level, which is specified. The distinction of the stepwise selection is that variables, which are already in the model, do not necessarily remain in it. Otherwise it is much similar to the forward selection one.
References
Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences . Abingdon-on-Thames: Routledge.
Harrell, F. (2015). Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis . New York , NY: Springer.
