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[Statistics] Suppose that we have n points (1, yı), -... (In: Yn) in the plane, and we wish to draw the most reasonable straight line through them. It is not likely that the line will be able to pass exactly through every point, but we would like it to be as "close as possible". Let y = a + ßx be the linear function that we use to go through these points, for a and 3 to be determined. There are various criteria we could use to determine what the "best" line is, but the most common is the least-squares line of best fit, also called the regression line. For this line, we seek to minimize the sum of the of the vertical deviations of the points from the line. (a) In everything that follows, remember that the r, and y, are the constants, and a and 3 are the variables. We seek the values of a and B (in terms of the r; and the y) which minimize f(a, B) =

[Statistics] Suppose that we have n points (1, yı), -... (In: Yn) in the plane, and we wish to draw the most reasonable straight line through them. It is not likely that the line will be able to pass exactly through every point, but we would like it to be as "close as possible". Let y = a + ßx be the linear function that we use to go through these points, for a and 3 to be determined. There are various criteria we could use to determine what the "best" line is, but the most common is the least-squares line of best fit, also called the regression line. For this line, we seek to minimize the sum of the of the vertical deviations of the points from the line. (a) In everything that follows, remember that the r, and y, are the constants, and a and 3 are the variables. We seek the values of a and B (in terms of the r; and the y) which minimize f(a, B) =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. [Statistics] Suppose that we have n points (21, y1), ... (In, Yn) in the plane, and we wish to draw the most reasonable straight line through them. It is not likely that the line will be able to pass exactly through every point, but we would like it to be as "close as possible". Let y = a + Br be the linear function that we use to go through these points, for a and 3 to be determined. There are various criteria we could use to determine what the "best" line is, but the most common is the least-squares line of best fit, also called the regression line. For this line, we seek to minimize the sum of the squares of the vertical deviations of the points from the line. (a) In everything that follows, remember that the r; and y4 are the constants, and a and 3 are the variables. We seek the values of a and B (in terms of the r; and the y:) which minimize f(a, 8) = (b) which we do by solving the following system af da af (c) to get the following values of a and 3: To keep the expressions from getting too messy, you can leave the expression for a in terms of 3 (so that if you ever need to solve for a, just plug the whole B expression into it). B = a =
Transcribed Image Text:4. [Statistics] Suppose that we have n points (21, y1), ... (In, Yn) in the plane, and we wish to draw the most reasonable straight line through them. It is not likely that the line will be able to pass exactly through every point, but we would like it to be as "close as possible". Let y = a + Br be the linear function that we use to go through these points, for a and 3 to be determined. There are various criteria we could use to determine what the "best" line is, but the most common is the least-squares line of best fit, also called the regression line. For this line, we seek to minimize the sum of the squares of the vertical deviations of the points from the line. (a) In everything that follows, remember that the r; and y4 are the constants, and a and 3 are the variables. We seek the values of a and B (in terms of the r; and the y:) which minimize f(a, 8) = (b) which we do by solving the following system af da af (c) to get the following values of a and 3: To keep the expressions from getting too messy, you can leave the expression for a in terms of 3 (so that if you ever need to solve for a, just plug the whole B expression into it). B = a =
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