assign_13_v2 - Georgia Southern University College of...

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Georgia Southern University College of Business Administration BUSA 3131, Business Statistics Fall 2011 Assignment 13 v.2 Name: ___________________ Simple Linear Regression, Computation of Estimated Regression Equation, Use of Excel The estimated regression equation is: y -hat i = b 0 + b 1 x i The objective of this equation is to use historical data describing values of two variables to estimate a trend line that accurately describes the relationship between the two variables. The trend line uses known observed values of x and y to extend the pattern of the trend line both above and below the range of known values of the two variables: x and y . In regression analysis, values of x are the independent variable and values of y are presumed to be the dependent variable. To create a trend line that can accurately represent the true relationship between two variables requires using a scatter diagram (or scatter plot) with a scale for values of x on the horizontal axis and a scale for values of y on the vertical axis. Plotting the intersection of values of x and y on the two axes makes it possible to observe a general trend. But using the estimated regression equation, permits the construction of a trend line that can estimate any value of y given a value of x . This predictive capability of simple linear regression is highly important for organizations in planning processes. Two components are needed to construct a trend line. The first defines the angle of the trend line relative to the horizontal axis. The trend line might tip upward from left to right, or it might tip downward from left to right, or it could be parallel to the horizontal line. An upward trend line reveals a positive relationship between the two variables. So, as values of x increase, so do values of y (although not necessarily at the same rate). A downward trend line indicates an negative relationship between values of x and values of y. Consequently, as values of x increase, values of y decrease. If different values of x have no effect on values of y, the trend line will be horizontal and parallel with the x axis and this would indicate no relationship between the two variables. In addition to knowing the angle between the trend line and the horizontal axis we need to know where on
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This note was uploaded on 01/30/2012 for the course BUSA 3131 taught by Professor Watson during the Fall '11 term at Georgia Southern University .

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assign_13_v2 - Georgia Southern University College of...

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