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Unformatted text preview: Econ 425 Introduction to Data, Matrices, and the Linear Regression Model Professor John Rust I. Statistics: a science whose goal is to formalize and improve our ability to make infer ences (i.e. learn about the world) from data. II. Where do we get data? A. Previously collected data from existing records: 1. Government records: IRS, Social Security, welfare rolls, etc. 2. Business records: Payroll records, annual reports, etc. 3. Personal records: Stock data, bills, receipts, employment histories B. Physical data from scientific observations/measurements: 1. Astronomical observations, e.g., Hubble space telescope 2. Weather observations: temperature readings, radar data 3. Archaeological findings, e.g., Dead Sea Scrolls C. Data from controlled experiments: 1. Physical experiments, e.g., smashing atoms in the Stanford Linear Accelerator, GMs auto crash tests, etc. 2. Human experiments, e.g., psychology experiments, laboratory experiments (dou ble auction and stock trading experiments, e ff ects of di ff erent incentive schemes), consumer panels (pizza taste tests) D. Data from surveys: i. 1. Harris/Gallup Polls, census surveys, socio/economic surveys III. Where do we go to get/find data? A. Library: Indices of reports and studies, e.g. Statistical Abstract of U.S. B. Data library: indices of machine readable data sets e.g. ICPSR holdings C. WWW: Downloading data from sites on the Internet D. Collect our own data IV. Types of survey data: A. Time series data: a single (individual/country/firm/etc.) followed over time B. Cross section data: Multiple (individual/countries/firms/etc.) recorded at a point in time C. Time series/Cross section data: A collection of crosssections of individuals at di ff erent points in time (not necessarily same individuals at di ff erent points of time) D. Panel data: A collection of individuals followed over time V. Machine Readable Data are typically stored as arrays of numbers. A. Definition: A twodimensional array of numbers is called a matrix . 1 1. A matrix has a certain number of rows and columns known as its dimension such as ( M N ), meaning that the matrix has M rows and N columns. 2. Matrices will typically be denoted by a capital letters, such as: X = [ x ij ] where the x ij denote the individual numbers in the matrix and the ( i,j ) denote the row and column indices of the matrix, respectively. 3. Example: x 23 denotes the element in the 2 nd row and the 3 rd column of the matrix X . B. Higher dimensional arrays These are arrays of numbers that have more than 2 indices. 1. Example: A 3dimensional array of numbers is given by X = { x ijk } , a four dimension array is given by X = { x ijkl } , etc....
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 Spring '06
 cramton

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