# MTH302 GDB Solution Spring 2012

CONSTRUCT A BUSINESS PROBLEM WHICH SHOWS A POSITIVE RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLES USING REGRESSION ANALYSIS

Solution:

Marketing research professionals often use inferential or descriptive statistics to guide major marketing decisions. There are a number of statistical tests that explore the relationship between the independent variable(s) and the dependent variable. The key is to translate the business problem into a statistical problem, solve the problem statistically, then translate the statistical solution into an actionable business solution.

## Dependent Variable

The dependent variable — also called the response variable — is the output of a process or statistical analysis. Its name comes from the fact that it depends on or responds to other variables. Typically, the dependent variable is the result you want to achieve. In marketing, the results desired are tied to sales revenue. Sales as a dependent variable can be looked at in many ways, such as sales of a specific doll, sales of a category like toy cars, overall sales at a particular store, or even sales for the entire company.

## Independent Variable

An independent variable is an input to a process or analysis that influences the dependent variable. While there can only be one dependent variable in a study, there may be multiple independent variables. When the dependent variable is sales revenue, the elements of the marketing mix — product, price, promotion and place — will definitely influence the dependent variable and can therefore be identified as independent variables.

## Regression Analysis in Marketing

Marketing research employs a statistical tool called regression analysis to measure the strength of the relationship between the dependent variable and the independent variables. For example, a frozen yogurt shop could set loyalty card discounts, base price, and time of day as the independent variables to test not only the direct effect each factor has on parfait sales, but whether there is interaction between the variables. If, when the base price is low, loyalty card discounts influence sales less than when the base price is high, there is an interaction between the two factors.

## Choosing the Right Variables

Asking the right question will lead you to the right answer. The more specific you can make your dependent variable — for instance, sales of a single MP3 player model as opposed to sales of all electronics — the better chance you have of isolating the independent variables that truly influence it. Also, even when you know your goal, you look at it a variety of different ways. For instance, “At what price can we make \$100,000 per quarter in sales of product A?” is a subtly different question than, “At a price of \$10, how many people will buy product A per quarter?” Look in the Resources section for further reading on how to start with the right question and use the right methodology to answer it.

A variable is an event, idea, value or some other object or category that a researcher or business can measure. Variables can be dependent or independent. Dependent variables vary by the factors that influence them, but independent variables stand on their own — changes in other variables have no effect on them. An independent variable in one context may be a dependent variable in another. An independent variable in business may affect sales, expenses and overall profitabilityIndependent variables that affect sales include customer demographics, store location and weather. Customer demographics include age, occupation, family status, income level and gender. These factors affect what a customer needs, which affects sales and ultimately profits. A store located in a densely populated metropolitan area may have higher sales than a store in a sparsely populated rural area. Similarly, customers may go shopping when the weather is pleasant, but few would venture outside in stormy or snowy weather. Some variables have a circular relationship with sales. For example, sales depend on advertising, but the level of advertising expenses also depends on sales.

## Expenses

The prices of raw materials, labor wage rates and facility rental rates are independent expense variables. The prices of raw materials, such as food commodities, metals and minerals, do not change, regardless of how much a small business spends on them. Labor wage rates and facility rental rates are other examples of independent expense variables. They affect the cost structure of a small business, but the owner cannot change market wage rates or rental rates by himself.

## Economy

Economic variables affect business profitability. The income of individual customers and profits of business customers are independent economic variables that affect overall business performance. During a recession, customers earn and spend less, which leads to declining business sales. Conversely, during a period of economic growth, customers earn and spend more, which increases business sales and profits. The interest rate on a bank loan or line of credit is an independent variable because it affects expenses and profits. However, the borrowing needs of a small business do not change interest rates.

## Considerations: Dependent Variables

In the business context, profit is a dependent variable because it depends on the economy, sales and expenses. Product quality depends on the manufacturing and design processes. The number of employees laid off during a recession depends partly on declining business revenues. Government tax revenue depends on customer income, business profits, capital gains and other variables.