{"id":3047,"date":"2024-04-24T09:00:12","date_gmt":"2024-04-24T16:00:12","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=3047"},"modified":"2020-01-15T10:50:18","modified_gmt":"2020-01-15T18:50:18","slug":"gmat-data-insights-correlation-and-trend-lines-in-scatterplots","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-data-insights-correlation-and-trend-lines-in-scatterplots\/","title":{"rendered":"GMAT Data Insights: Correlation and Trend Lines in Scatterplots"},"content":{"rendered":"

\"DI
\nOne reason we graph data in a scatterplot is because we are looking for patterns.\u00a0 The simplest of all possible patterns to find on a scatterplot<\/a> is a straight line pattern.<\/p>\n

Correlation<\/h2>\n

When the points on a scatterplot lie more or less in a straight-ish line, that is called correlation<\/strong>.\u00a0 When it’s a straight line with a positive slope, going up to the right, that’s positive correlation<\/strong>, and when it’s a negative, slope, that’s negative correlation<\/strong>.\u00a0 To say that A and B have a positive correlation is to say that when A goes up, B goes up.\u00a0 Here’s an example of a graph with a very strong positive correlation.<\/p>\n

\"\"<\/a><\/p>\n

Notice, the points are not perfectly in a line, but the upward trend is unmistakably clear.\u00a0 In the real world, examples of variables that are positively correlated are the price of crude oil per barrel & the price of a gallon of gasoline; the number of automobiles in a municipality & the number of traffic lights in that municipality; daily temperature & daily ice cream sales; etc.<\/p>\n

Here’s another example graph, with a very clear negative correlation.<\/p>\n

\"\"<\/a><\/p>\n

Again, the points do not line in a perfect straight line, but the downward trend is clear: when the x-axis variable goes up, the y-axis variable does down.\u00a0 In the real word, examples of variables that are approximately negatively correlated are the unemployment rate & the Dow Jones average; the torque of a car’s engine & its fuel efficiency; a baseball pitcher’s career ERA & his number of career shutouts; etc.<\/p>\n

Those two graphs were, by statistical standards, quite “pretty”: the pattern is very clear, and little of real-world messiness is evident.\u00a0 Here’s some real-world data, exploring that last baseball point: a baseball pitcher’s career ERA vs. his number of career shutouts.<\/p>\n

\"\"<\/a><\/p>\n

This graph only includes career leaders (in the top 1000) in both stats.\u00a0 It’s much messier than the previous graphs, which is typical of real world data, but the negative trend is still apparent.\u00a0 BTW, that single dot way up at the top, with Career Shutouts = 110 and a career ERA = 2.17, is the great Walter Johnson<\/a>, easily one of the finest pitchers of all time.<\/p>\n

 <\/p>\n

Trend Lines<\/h2>\n

For the first two graphs, we can easily imagine the straight line that would go through these points and summarize them. It’s somewhat less clear exactly where it would lie on the third “messy graph.\u00a0 This line, which summarizes the implicit linear trend in a scatterplot is called alternately a “trend line” or a “line of best fit.”\u00a0 The official name in statistics is a “least square regression line”, but the exact details about how it is calculated and all its technical properties are well beyond what you need to understand for the GMAT.<\/p>\n

Here’s the second graph again, with a trendline.<\/p>\n

\"\"<\/a><\/p>\n

The trend line moves through the center of the linear pattern.\u00a0 Here, the points are negatively correlated, so the trendline has a negative slope.<\/p>\n

Here’s the baseball graph with its trend line.<\/p>\n

\"\"<\/a><\/p>\n

The trendline allows us to make prediction of a typical data point.\u00a0 For example, here, if a pitcher has a career ERA of about 3.50, we would expect that pitcher to have, on average, about 20 career shutouts.\u00a0 Pitchers above the trendline had more shutouts than expected for their ERA, and pitchers below the trendline had fewer shutouts than expected for their ERA.\u00a0 Making a predicted y-value for a hypothetical x-value, or judging whether an individual point has a higher or lower “typical” y-value, given its x-value — this is about all the trendline analysis the GMAT will expect of you.<\/p>\n

 <\/p>\n

A Word about Correlation<\/span><\/h2>\n

This caution, about the meaning of correlation, may be more relevant to GMAT Critical Reasoning that it is to Data Insights.\u00a0 To say A and B are positively correlated is to say: when A is a relatively big number, so is B; and when A is a relatively small number, so is B.\u00a0 A and B “go together.”\u00a0 What it does not<\/em><\/strong> mean is: A causes B.\u00a0 If A causes B, or if B causes A, then the two variables will have a high correlation, BUT the converse is not true.\u00a0 As the canonical saying in the social sciences goes: correlation does not imply causality<\/span><\/strong>.\u00a0 Just because A and B appear together does not necessary mean that A directly causes B or vice versa; it may mean that both are caused by another factor, or there may be a more complex relationship.\u00a0\u00a0 Inferring causality from correlation is a classic social science mistake: keep an eye out for this in “flawed arguments” on CR questions.<\/p>\n

 <\/p>\n

Practice Question<\/h2>\n

Here’s a free practice question involving a scatterplot with a trendline.<\/p>\n

1) http:\/\/gmat.magoosh.com\/questions\/2305<\/a><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

One reason we graph data in a scatterplot is because we are looking for patterns.\u00a0 The simplest of all possible patterns to find on a scatterplot is a straight line pattern. 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He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3047","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=3047"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3047\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=3047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=3047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=3047"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=3047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}