Introduction
I am a consultant to Diligent Consulting Group. In this case, consultations were conducted with an organization called Loving Organic Foods. To better understand what might motivate shopping habits, I was tasked with analyzing the factors that influence the cost of organic food. To achieve this, I decided to use linear regression analysis.
Regression analysis is one of the most popular statistical research methods. It can be used to set the degree of influence of independent variables on the dependent ones. Winston (2019) claims that by analyzing and examining the raw data, the researcher can make and come to inferences, compare and contrast, or even classify the data based on a specification attribute. Using statistical regression techniques is one of the most effective ways to examine these attributes properly. Moreover, according to Zhou (2020), it may be necessary to apply the concepts of correlation and linear regression equations. Once enough data has been collected and analyzed, the attributes with the most and least significant data can be identified.
Before proceeding to the analysis of data, it is vital to identify the variables. In this study, variables such as Annual Amount Spent on Organic Food and consumer Age are used. In this case, the independent variable (x) is Age, and the dependent variable (y) is the Annual Amount Spent on Organic Food.
Interpretation of the obtained results
The regression output generated in Excel
- Multiple R = 0, 114912552
- R Square = 0, 013204895
- Adjusted R Square = 0, 00511641
- Standard Error = 3718, 777442
- Observations = 124
Interpretation of the coefficient of determination (R-squared)
R-squared statistically measures the closeness of the data to the fitted regression line. The R-squared is 0,013, which means the model describes 1, 3% variability in the response data based on its mean.
Interpretation of the coefficient estimate for the Age variable
The correlation coefficient is the square root of the R-squared value. It is used to measure how strong the relationship is between two variables.
Interpretation of the statistical significance of the coefficient estimate for the Age variable
A correlation coefficient of 0, 114 shows a weak positive relationship between the Annual Amount Spent on Organic Food and Age.
Furthermore, there is a block of information containing hypothesis tests for a particular coefficient.
Since there are p-values corresponding to Age (0, 204) > 0, 05, their presence in this regression model is negligible. Based on this, it can also be concluded that there is no strong relationship between the Annual Amount Spent on Organic Food and Age. Moreover, Alexander et al. (2017) note that the variable Age is not statistically significant based on the correlation coefficient.
The regression equation with estimates substituted into the equation
y = 9778, 28 + 26, 29x
According to Winston (2019), the coefficient of Intercept indicates what value Y will have with all other factors equal to zero. Zhou (2020) asserts that the coefficient of Age shows the level of dependence of Y on X. In this case, it is the level of dependence of the Annual Amount Spent on Organic Food on the Age of consumers.
The slope of the equation 26,29 tells us that increasing Age enlarges the Annual Amount Spent on Organic Food by 26,29, and the intersection point Y, 9778,28 is the initial Annual Amount Spent on Organic Food.
An estimate of Annual Amount Spent on Organic Food for the average consumer
Recall that the “average” customer is one that is close to 48 years old and spends an average of 11046 dollars a year on organic food. This indicator corresponds to the mean.
Y = 9778, 28 + 26, 29 * 48 = 11040, 2
Thus, the Annual Amount Spent on Organic Food for the average consumer is 11040, 2.
Conclusion
Regression analysis is a set of statistical methods for evaluating relationships between variables. It can be used to assess the degree of relationship between variables and to model future dependencies. In fact, regression methods show how the change in the dependent variable can be recorded based on changes in the independent ones. With the help of analysts, the correlation coefficient is deduced, which means the strength of the connections. The more significant it is, the easier it is to create a regression model.
As a result of the conducted research, it can be concluded that there is no strong relationship between the Annual Amount Spent on Organic Food and Age. The coefficient of determination is 0, 013, which means that there is 1, 3% of the total variation in the sample of the Annual Amount Spent on Organic Products. When the variable Age increases by one unit while keeping the other dependent variables constant, the Annual Amount Spent on Organic Food increases by 26, 29 units.
References
Alexander, H., Illowsky, B., & Dean, S. (2017). Introductory business statistics. Openstax.
Winston, W. (2019). Data analysis and business modeling. (6th ed.). Microsoft Press.
Zhou, H. (2020). Learn data mining through excel: A step-by-step approach for understanding machine learning methods. Apress.