Simple Linear Regression Model
Loving Organic Foods Company wishes to better their products and also have a better understanding of their customers. By understanding their customers’ behaviors, they will be able to make larger sales of organic food. To achieve this, I will base my analysis on what is the driving force of the customers on the buying of organic foods. To get a better idea of this, I will look at the underlying variables that impact organic foods’ consumption. To get the relationship between these factors, I will use a linear regression model.
Regression models usually describe the relationship between different variables by fitting the line of best fit to the data (Holmes, 2018). Linear regression models use a straight line to fit the observed data. The linear regression model estimates the relationship between two given variables, mostly referred to us as the X variable and Y variable. It is used to determine how strong the relationship is between the X variable and Y variable. It is also used to determine the value of the dependent variable, Y, at a given independent variable, X. In simple terms is used for the estimation of the dependent variables. The regression model’s importance is that it helps determine those factors that matter most and those factors that should not be considered. Therefore, it makes it easier to study the relationship between different factors under study, and also it enables a business to make the right decisions from the observed data (Holmes, 2018).
I fitted a simple linear regression model on the data, which has the dependent variable as the Annual amount spent on organic foods, and the independent variable is the age. I fitted the regression line using Microsoft Excel, the best tool (Fraser, 2016). The Excel output is as follows: y = 26.293x + 9778.3.
Interpretation of the Coefficient of Determination
In the analysis, I also computed the coefficient of determination (r squared). The value of the coefficient of determination is 0.0132. The coefficient of determination is a measure used in the regression model to determine the portion of the variance in the dependent variable, which can be explained in the independent variable. It tells us how efficient the model is. As we can see, our coefficient of determination is very low. It is about 1%. This is likely because of the noise that is found in our data. The outliers tend to reduce the coefficient of determination to be very small. This is to say, despite the variabilities, the trend line still exists and can be used to predict the data.
Interpretation of Coefficient Estimate of Age
The coefficient estimate for the age estimate is the 26.293. This means that a 26.293 is the gradient of our line or the slope, which interprets how steep the line of regression is. Our slope, in this case, is positive. Every time we increase the age by one unit, the annual amount spent on buying organic food will be increased by an average of 26.293. This is a positive increase, which means that as the age of the customer increases, the amount spent on buying organic foods also increases. Therefore, the consumption of organic foods is increasing as the age of the customers’ increases. This is statistically significant.
Regression Equation
When the estimates are substituted into the equation, the regression equation will look as follows: Annual amount spent on organic food = 9778.3 + 26.293 * Age. In the estimation of the annual expenditures on organic food can be estimated using the above regression equation. The estimation can be done by first finding the value of the ages of the customers who are under the study. The ages of these customers will then be multiplied by the age variable’s coefficient, which is the slope of our line of best fit (Fraser, 2016). After that, the value obtained after the multiplication will then be added to the y-intercept, in which our case is 9778.3. the y-intercept is the value of the annual expenditures at the age of zero. After the addition, the value that we obtain becomes our estimate of the annual expenditures on the organic food by the respective customers who are of that age.
To get a better picture of this, I wish to compute the annual amount spent on organic food for an average consumer. To get an average consumer, I computed the average age of the consumers of organic food. The average age is 48.2339, rounded to four significant figures. When the average age is substituted in the linear estimation equation, we have the following: Annual amount spend on organic food = 9778.3 + 26.293 * 48.2339. When the above equation is solved, we will have 11,046.5139. Therefore, this means that an average consumer is likely to spend around 11,046.5139 annually on organic food. This is a very good amount, and this is a positive indicator of the business. Therefore, the business needs to focus more on average consumers. This is to ensure that more profits are realized in the business. Aside from that, the business should also focus more on older people since they are more likely to spend a lot of money buying organic foods.
References
Holmes, A., Illowsky, B., & Dean, S. (2018). Introductory business statistics.
Fraser, C. (2016). Business statistics for competitive advantage with Excel 2016: Basics, model building, simulation and cases. Springer.