{"id":9003,"date":"2016-06-18T03:00:20","date_gmt":"2016-06-18T03:00:20","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=9003"},"modified":"2016-06-18T03:00:20","modified_gmt":"2016-06-18T03:00:20","slug":"math-review-of-fitting-equations-to-data","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-fitting-equations-to-data\/","title":{"rendered":"Math Review of Fitting Equations to Data"},"content":{"rendered":"

Overview<\/h3>\n

Many real-world situations can be approximated by the relationship between two different variables that fall on a straight line. The linear equation is one model of the data.\u00a0 Sometimes the task is to predict another value from a small amount of data, while other times it is to find a relationship between large amounts of data.\u00a0 The task is always to understand the problem, make a plan, find the answer, and check.<\/p>\n

The Point-Slope Equation<\/h3>\n

Recall that if the coordinates of one point on a line and the slope of that line are known, the equation for that line can be derived by using the slope to find another point on the line.\u00a0 Suppose that one point on a line has the coordinates (1, 3) and the slope of the line is 2.\u00a0 Any other point on the line will have the coordinates (x, y).\u00a0 The difference of the y coordinates is (y -3) and the difference of the x coordinates is (x-1).\u00a0 Therefore, (y-3)\/(x-1) equals 2, because we already know that the slope is 2.\u00a0 If both sides of the equation are multiplied by (x-1) to get the (x-1) out of the denominator, then 2(x-1) = y-3, or 2x-2 = y-3, and 2x-2 +3 = y.\u00a0 Therefore, 2x +1 =y and that is the equation of the line. \u00a0Another way to say this in general is the point-slope equation:\u00a0 y-y1<\/sub> = m(x-x1<\/sub>).<\/p>\n

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Organizing Data<\/h3>\n

There are different ways to organize data to make their relationship more clear.\u00a0 Perhaps there are just one or two ordered pairs of data to calculate from, and it is reasonable to assume that the relationship is linear.\u00a0 The point-slope equation might be a good option.<\/p>\n

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Line of Best Fit<\/h3>\n

Suppose there are many ordered pairs.\u00a0 A chart could be drawn of the data, and the ordered pairs could be plotted.\u00a0 At that point, a line could be drawn through the data so there are about as many data points above the line as below the line.\u00a0 This is referred to as the line of best fit.<\/p>\n

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Applications<\/h3>\n

Many different types of data can be described as ordered pairs on a graph.\u00a0 In the graph above for the line of best fit, the year is shown as the x-coordinate and the sea level is shown as the y-coordinate.\u00a0 Sports records can be shown from year to year.<\/p>\n

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Overview Many real-world situations can be approximated by the relationship between two different variables that fall on a straight line. The linear equation is one model of the data.\u00a0 Sometimes the task is to predict another value from a small amount of data, while other times it is to find a relationship between large amounts […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2688,3964,3963],"class_list":["post-9003","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-line-of-best-fit","tag-organizing-data","tag-point-slope-equation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=9003"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9003\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=9003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=9003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=9003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}