linalg - Econ 425 Introduction to Data, Matrices, and the...

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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 cross-sections 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 two-dimensional 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 3-dimensional array of numbers is given by X = { x ijk } , a four dimension array is given by X = { x ijkl } , etc....
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linalg - Econ 425 Introduction to Data, Matrices, and the...

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