# Project #4063 - Core Project

Math Core Project       The individual   project for this class is linear regression : finding the best - fitting line for a set of ordered pairs (x, y) and then using the equation of that line to predict a new y - value for a given x - value. The first step in thi s process is determining if there is a strong linear correlation among the ordered pairs . I f the points come close to forming a straight line   when plotted on a coordinate   plane, there is a strong linear correlation .   You will be using Microsoft Excel for this project.       1. Explanation of Data and Source   For this project you will use population data. Look up the population of a city, county, state, or country   for the past 5 years. For each data pair, let x represent the number of years after 2000 and le t y represent   the population for that year. Explain the source of the data an d what it represents .   (NOTE: A good   source of population data is www.recenter.tamu.edu . Click “Data” and then “Population” to ob tain data.)       2.   Data   Table with x and y Properly Identified     Present the pairs of numbers in table form. If you are doing a project with years, you must   set up a     correspondence such as x = the number of years after ____ (your starting ye ar). This mus t be done     because you cannot break the x - axis on the graph. For this project you are using population data for the     past 5 years. Therefore, you will use the correspondence x = the number of years after 2000. List the x -     values and the years they re present in the x column. List the population for each year in the y column.       3. Correlation Coefficient     The correlation coefficient (r) is a measure of the linear correlation of the data (i.e., how close the data     points come to forming a straight lin e). The correlation coefficient is a number between - 1 and 1. If r is   close to 0, it means there is little correlation (bad data set). If r is close to 1 , it means there is a strong   positive correlation (the y - values are increasing). If r is close to   - 1, it means there is a strong negative   correlation (the y - values are decreasing) .   The value of the correlation coefficient also indicates how   accurately the regression equation can be expected   to predict future outcomes.     Calculating the Correlation C oefficient (r) in Excel 20 10   Click on the Page Layout tab. Click on Orientation. Click on Landscape.   Enter the x – values in column A. Enter the y – values in column B.   Click on cell D1, and click on Insert Function (fx).   Select the category Statistical. ( Click on it.)   Select a function: CORREL. (Click on it and then click OK.)   Click in the box for Array1.   Highlight the x−values; when you release the mouse button, they should be entered   automatically .   Click in the box for Array2.   Highlight the y−values ; w hen you release the mouse button, they should be entered   automatically .   Click OK. The correlation coefficient of the data should   appear in cell D1. In cell   E1 , type an “r” to     label this value as the correlation coefficient.

 Subject Mathematics Due By (Pacific Time) 04/07/2013 12:00 am
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