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Permalink Reply by Yasmeen(S.admin) on July 3, 2012 at 11:14am

Regression Analysis

Regression analysis allows you to model, examine, and explore spatial relationships, and can help explain the factors behind observed spatial patterns. Regression analysis is also used for prediction.

Regression equation: this is the mathematical formula applied to the explanatory variables in order to best predict the dependent variable you are trying to model. Unfortunately for those in the Geo-sciences who think of X and Y as coordinates, the notation in regression equations for the dependent variable is always "y" and for independent or explanatory variables is always "X". Each independent variable is associated with a regression coefficient describing the strength and the sign of that variable's relationship to the dependent variable. A regression equation might look like this (y is the dependent variable, the X's are the explanatory variables, and the β's are regression coefficients; each of these components of the regression equation.

Y =  βο + β1X1 + β2X2 + ……………………………+ βnXn +  ε

Y = Dependent variable

Βο, β1, β2 ……………..βn = Regression Co-efficients

X1, X2,…………………Xn = Explanatory Variables(independent)

ε  = Random Error Term / Residuals.

 

 Dependent variable (y): this is the variable representing the process you are trying to predict or understand (e.g., residential burglary, foreclosure, rainfall). In the regression equation, it appears on the left side of the equal sign. While you can use regression to predict the dependent variable, you always start with a set of known y values and use these to build (or to calibrate) the regression model. The known y values are often referred to as observed values.

  Independent/Explanatory variables (X): these are the variables used to model or to predict the dependent variable values. In the regression equation, they appear on the right side of the equal sign and are often referred to as explanatory variables. We say that the dependent variable is a function of the explanatory variables. If you are interested in predicting annual purchases for a proposed store, you might include in your model explanatory variables representing the number of potential customers, distance to competition, store visibility, and local spending patterns, for example.

  Regression coefficients (β): coefficients are computed by the regression tool. They are values, one for each explanatory variable, that represent the strength and type of relationship the explanatory variable has to the dependent variable. Suppose you are modeling fire frequency as a function of solar radiation, vegetation, precipitation and aspect. You might expect a positive relationship between fire frequency and solar radiation (the more sun, the more frequent the fire incidents). When the relationship is positive, the sign for the associated coefficient is also positive. You might expect a negative relationship between fire frequency and precipitation (places with more rain have fewer fires). Coefficients for negative relationships have negative signs. When the relationship is a strong one, the coefficient is large. Weak relationships are associated with coefficients near zero.

β₀ is the regression intercept. It represents the expected value for the dependent variable if all of the independent variables are zero.

Residuals: these are the unexplained portion of the dependent variable, represented in the regression equation as the “random error term, ε”. Known values for the dependent variable are used to build and to calibrate the regression model. Using known values for the dependent variable (y) and known values for all of the explanatory variables (the Xs), the regression tool constructs an equation that will predict those known y values, as well as possible. The predicted values will rarely match the observed values exactly. The difference between the observed y values and the predicted y values are called the residuals. The magnitude of the residuals from a regression equation is one measure of model fit. Large residuals indicate poor model fit.

Building a regression model is an iterative process that involves finding effective independent variables to explain the process you are trying to model/understand, then running the regression tool to determine which variables are effective predictors… then removing/adding variables until you find the best model possible.

Permalink Reply by Yasmeen(S.admin) on July 3, 2012 at 11:24am

Correlation & Regression - Relationship Analysis

Permalink Reply by Yasmeen(S.admin) on July 3, 2012 at 11:37am

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.

Permalink Reply by Doctor on July 4, 2012 at 7:46am

thanks

but its very lengthy.

 

Permalink Reply by Yasmeen(S.admin) on July 4, 2012 at 11:26am

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Permalink Reply by SiLeNt MooN(Admin) on July 4, 2012 at 1:20pm

open the attach file for the solution

• New Microsoft Word Document.doc, 51 KB