Often times we have a large collection of explanatory

This preview shows page 109 - 114 out of 114 pages.

Often times we have a large collection of explanatory variables and our aim is to determine which combination of them best describes the variability in our response variable. Our model : ? = ? 0 + ? 1 ? 1 + ? 2 ? 2 + ⋯ + ? 𝑝 ? 𝑝 + ?
Where ? 1 , ? 2 , … , ? 𝑝 are ? explanatory variables which are assumed “fixed”. ? 0 , ? 1 , ? 2 , … , ? 𝑝 are ? + 1 parameters (regression coefficients) which are unknown ? represents our random component (random error) having a mean of 0 and constant variance, 𝜎 2 . Errors for different cases ( ? ? , ? ? ) are assumed independent.
Example Market value of unsold property Determine market value based on values of similar properties. Explanatory variables include size, age, percent office, building/land ratio, location The model is used to predict market values for houses not included in the model. If you have many explanatory variables, which should you include? Should you include all properties? Foreclosures?
Example: Capital Investment Capital investment occurs when a business person believes that a profit can be made. Thus, capital investment is a function of variables related to the potential for profit, including interest rate, gross domestic product, consumer expectations, disposable income e.t.c
Example: Retail Location Large retail companies decide on locations for new outlets based on the anticipated sales revenue and/or profitability. Using data from previous successful and unsuccessful locations, analysts can build models that predict sales or profit for a potential new location. Size of the store Traffic volume on road in front of store Stand-alone store vs. shopping mall location Location of competing stores within 500m radius Total number of people within 20km radius
Example: Office Overhead Costs A service organization has 24 offices An auditor assesses overhead costs for offices Information about office size, age, number of employees; number of clients; cost of living index for the location The auditor wants to spend more time on offices that have an unusual overhead The auditor is looking for outliers explanatory variables will affect overhead can’t just pick the largest or the smallest.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture