Executive summary
Multiple linear regression analysis is a statistical tool of analysis that is commonly used to forecast a variable, which is dependent on several independent variables based on historical data. Multiple linear regression analysis is normally used to evaluate the nature of the correlation between the dependent variable denoted as y and the independent variables (X1, X2Xn). The developed model is then used to predict levels of the dependent variable y. Multiple linear regressions is important in business, economics, medicine, psychology among many other fields.
The correlation between Y predicted and Y actual is called the multiple correlation coefficients which is symbolized by R. R measures how well a given set of independent variables can be used to predict Y. In other words, it measures the explanatory power of the model
Introduction
Multiple linear regression analysis is normally used to predict the future and in analyzing the dependent variable determinants. Multiple linear regressions analysis is important in business, economics, medicine, psychology among many other fields. In this case, we will analyze how multiple linear regression analysis can be used in business to analyze sales.
Sales level is influenced by several factors. These factors include price of the product, population, competitor prices, advertisement, season, time among others. Business must beware of the determinants of sales and how significant each of the determinants is in order to effective make operational and strategic decisions. The management will therefore save time and resources by focusing their energies on variables that significantly influence sales while ignoring the ones that are less significant. Performing multiple regression analysis on sales data and the determinants will, therefore, be important for any firm that seeks to have a competitive edge and remain relevant by continually improving on aspects that influence their sales level. This research seeks to analyze the determinants of sales volume of Peterson fruit Pie Company in Chicago to help their management in making strategic and operation plans in the future.
Objective
The purpose of this research paper is to establish the determinants of sales volume of Peterson fruit Pie Company in Chicago and how significant each of the determinants is. Four variables were recognized that are expected to influence sales level; price of the good, price charged by competitors, advertisement and time variable. Multiple regression analysis will be used to determine the extent to which the four variables determine the number of units sold. The multiple regression analysis will also be used to predict the future sales units given the levels of the four explanatory variables.
Methodology
This research will use secondary data to obtain the data required for the analysis. The past quarterly income statement provided the relevant data on price of the good, price charged by competitors, advertisement for the twelve quarters used in the analysis from quarter beginning January 2009 to the quarter December 2011. The time variable is assumed to progress arithmetically with first quarter of 2009 being 1 and the last quarter of 2011 being 12
The model will have four explanatory variables; price of the good, price charged by competitors, advertisement and time variable. Assuming that price of the good is represented by X1 , prices charged by competitors is X2 , advertisement is represented by X3 and time variable is represented by X4. Then the regression equation will be;
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4
Where; β0 is the constant term and β1 ,β2 ,β3 and β4 are the coefficients of price of the good, price charged by competitors, advertisement and time variable respectively.
Fundamentals of multiple linear regression analysis
Multiple linear regression analysis is a statistical tool of analysis that is commonly used to forecast a variable that is dependent on several independent variables based on historical data. Multiple linear regression analysis is normally used to evaluate the nature of the correlation between the dependent variable denoted by y and the independent variables. The developed model is then used to predict levels of the dependent variable y.
The correlation between Y predicted and Y actual is called the multiple correlation coefficient which is symbolized by R. R is a measure of how well a given set of independent variables can be used to predict Y. In other words, it measures the explanatory power of the model.
Testing of hypothesis
T-test is normally performed to determine whether the individual coefficients of the dependent variables are statistically significant. In performing data analysis normally samples are used because of the numerous advantages that accrue from using a sample instead of the whole population. The smaller the sample, the higher the observed correlations are likely to vary from the population values. T-test, therefore, determine whether a variable is statistically significant after factoring in the sample size used in the analysis. The t-statistic obtained from the regression output is compared to the t-critical obtained from the t-distribution tables at the given confidence level and degrees of freedom. If the t-statistic is higher than the t-critical then the variable is statistically significant. However, if the t-statistic is lower than the t-critical then the variable is not statistically significant.
Adjusted R square is a measure of the explanatory power of the model. The adjusted R square of 0.8996 implies that 89.96% of the variation in the units sold by Peterson fruit Pie Company can be explained by the model. The model has eleven degrees of freedom; 4 due to regression and 7 due to the residual term.
The coefficient of the price of fruit pie is -95,317.99. It has a negative sign; this implies that there is an inverse relationship between the price of fruit pie and the number of units of fruit pie sold. The coefficient of 95,317.99 implies that a unit change in price will cause the number of units sold to change by 95,318.
The coefficient of competitor’s price of fruit pie is 75,551.5339. It has a positive sign; this implies that there is a direct relationship between competitor’s price and the number of units of fruit pie sold. The coefficient of 75,551.5339 implies that a unit change in price will cause the number of units sold to change by 75,552.
The coefficient of advertisement of fruit pie is 0.86700639. It has a positive sign; this implies that there is a direct relationship between advertisement and the number of units of fruit pie sold. The coefficient of advertisement is 0.86700639, this implies that a unit change in price will cause the number of units sold to change by 0.86700639.
The coefficient of time variable is 24343.4745. It has a positive sign; this implies that there is a direct relationship between time variable and the number of units of fruit pie sold. The coefficient of time variable is 24343.4745, this implies that a unit change in price will cause the number of units sold to change by 24343.4745.
T- Critical can be determined from the t-distribution tables. From the table, at 95% confidence level with eleven degrees of freedom, the t-critical is 2.201.
The t-calculated from the regression output of the constant term is 1.579873099 which is below 2.201. Therefore, the constant term is not statistically significant.
The t-calculated from the regression output of the price of fruit pie is -4.55194121 which is above the t-critical of 2.201 in absolute terms. Therefore, the price of fruit pie is statistically significant.
The t-calculated from the regression output of the competitor’s price of fruit pie is 4.155221382 which is above the t-critical of 2.201 in absolute terms. Therefore, competitor’s price of fruit pie is statistically significant.
The t-calculated from the regression output of advertisement is 3.560598221 which is above the t-critical of 2.201 in absolute terms. Therefore, advertisement is statistically significant.
The t-calculated from the regression output of time variable is 8.447457197which is above the t-critical of 2.201 in absolute terms. Therefore, advertisement is statistically significant.
The multiple regression analysis clearly indicates that multiple regression model is generally significant. Therefore, the model is applicable in analyzing the determinants of sales in Peterson fruit Pie Company. The multiple regression analysis can also be useful in predicting future sales levels of Peterson fruit Pie Company.
I would advise the management of Peterson fruit Pie Company implement price cuts since the units sold change significantly with a change in prices. I would also advice Peterson fruit Pie Company to do away with advertisement since a change in advertisement causes a change in the sales units by less than a unit.
Complex of topics
The sine qua non of success
Comments / Suggestions
General Economis
Which macroeconomic relevance is inherent in the topics?
The topic has macroeconomic relevance since it analyses the determinants of demand. If the sales volume of all firms is added then we obtain the aggregate demand.
How is the topic´s strategic relevance to be evaluated, especially concerning the aspects of securing existencs, competitive advantages, tying up resources, sustainability, and risk?
Business must beware of the determinants of sales and how significant each of the determinants is in order to effective make strategic decisions. Management will, therefore, concentrate on improving factors that will increase their sales units thus securing the existence of the business and ensuring continued competitive advantage.
What advantages and disadvantages arise out of the suggestions for marketing measures, external impact, and the company´s general productivity?
Which measures should be taken concerning internal and/or external marketing?
Implementing price cuts will significantly increase the sales volume. Eliminating advertizing will reduce the sales revenue but to a small extend.
The company should therefore reduce prices and eliminate advertisement
Financial Management
What criteria have to be considered when choosing appropriate terms of financing?
Which risks are there and what kind of coverage do you suggest? How should the influence of external factors be evaluated.
The risk inherent to means of financing are interest rate risk and liquidity risk.
The influence of external factors can be evaluated using the terms of the borrowing contract, past experience and the nature of the finance.What personnel consequences (quantitative or qualitative) result from the suggestions?
Eliminating advertisement may lead to redundancies which will necessitate sucking some employees.Which legal fields are affected by the suggestions? What has to be arranged in order to create legal security from the company´s point of view?
The company will have to comply with laws regarding laying off employees whose services are no longer needed by the company. The company will incur several costs as a consequence for example the company will be required to pay for a two month salary to each employee in addition to severance pay.
Management Decision Making
What sources of information should be practised in order to stay up to date in the fields of topics? Which decision criteria should be practised on the choice of alternatives?
The company can search for information from market research firms. It is easier to source for information from market research firms because they will provide the exact information required thus saving on time and other resources.
What demands does the realisation of the suggestions make on responsible managers? What leadership behaviour is expedient?
The management need soft skills in order to communicate with the employees who have to laid off to undertsand the position of the company and why it came to that decision.
