{"id":6473,"date":"2021-10-30T07:40:40","date_gmt":"2021-10-30T07:40:40","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=2923"},"modified":"2025-12-14T09:29:55","modified_gmt":"2025-12-14T03:59:55","slug":"what-is-correlation-why-it-is-so-important","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-correlation-why-it-is-so-important\/","title":{"rendered":"What is Correlation? Why it is so important?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Overview<\/strong><\/h2>\n\n\n\n<p>Correlation is the measurement of the strength of a linear relationship between two variables say x and y.<\/p>\n\n\n\n<p>In other words, we define it as if the change in one variable affects a change in other variables, then these two variables are said to be correlated.<\/p>\n\n\n\n<p>For example:<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; The correlation between a person\u2019s income and expenditures.<\/p>\n\n\n\n<p>2. &nbsp; &nbsp; As the temperature goes up, the demand for ice cream also goes up.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Types of correlation<\/strong><\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Bg6-38J9XV79V6cLnrdnH-md-EWC3ev3BAQqIXmZKIIraDnbAn7C-Y7ogIShXG4GQEHZoLo3B2DHLhr-MIVchZdpKdz70iTF0e8ckKjEz4OopA78vDHVhFk5Y9TbZGDB3YBX8Kts\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>Positive correlation-<\/strong> When both variables move in the same direction, or if the increase in one variable results in a corresponding increase in the other one is called positive correlation.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/StzCSJZV_EmEOtjg138sWT7snxWn8GNELeumOkow3oqn_KrI80yrLqA0igVu2MPSp50gtyiHZVmYH50iqOFBC7C4-tcHWzOuo4hxkW9WBl1PkvxSdkaksQVZOn_F3GCa78vT0FHW\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>Negative correlation- <\/strong>When one variable increases and other decreases or vise-versa, then the variables said to be negatively correlated.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/SlifM3uAMAeEwIhdMe4S1sVWt6DLuKelRVhfc-qJI4VLDAnEYTbhrAg4K8nkxslzY3GfT-ugu1sVtBUrJfyH0rHsve2enssR82qGv53MhBgHtn36A-AaO9UGjcw4x5LlFbLXm00k\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>No correlation- <\/strong>When two variables are independent and do not affect each other then there will be no correlation between the two and said to be uncorrelated.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/lIx4NUEJe4JXo4eKRusmswsZSx-TvL3cSu2q60f37JO9llSXj8UzMnrFgwHEahn7u7dFCx2wYKzBoNcvASbho_stjig4O-7Wv_t5MAeLQuue8CJngYYyekHTx2FsTx5XOCGlLSX5\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>Note- (Perfect correlation)- <\/strong>When a variable changes constantly with the other variable, then these two variables are said to be perfectly correlated.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Scatter plots or dot diagrams<\/strong><\/h2>\n\n\n\n<p>A scatter or dot diagram is used to check the correlation between the two variables.<\/p>\n\n\n\n<p>It is the simplest method to represent bivariate data.<\/p>\n\n\n\n<p>When the dots in the diagram are very close to each other, then we can say that there is a fairly good correlation.<\/p>\n\n\n\n<p>If the dots are scattered then we get a poor correlation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Karl Pearson\u2019s coefficient of correlation<\/strong><\/h2>\n\n\n\n<p>Karl Person\u2019s coefficient of correlation is also called product-moment correlation coefficient.<\/p>\n\n\n\n<p>It is denoted by \u2018r\u2019, and defined as-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/WJj70gSq6smijhUVOsxmlCYwxOhgOubrkhdx8rCdFmZPu5dQ_19eTQURaUyM71U327kVIaZiAjmOUvokQvzENXmr_p1mb7uSIniZX8I6RhWzDmrnYtqtwAw0pNBMMMLpNq3YJMOd\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Here <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Fuv3vVcMEBUsg9EE9VVLsSHr1J-9adoBQTE1jT8Xr73oDpQS3UyORcgV0hN1fABBdIj7OU-QWxEcAtSZwMncXICkJC_CUm-ZY2ANS5BtudTCUFv9Itc5JpVTvTE7p_ne491ZPXOc\" width=\"21\" height=\"22\">and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/w4294XY_YGKC-XTjj702jbKHTeYOUDOYImi-yTuC7y53UpsPWjC7QLl0nZt3Ie1zh7zIL5WdvEa3BlM2HFLUv2Bl0qPbf0yHUQ3SWZ9yxzzphTEIkldDIj3teZ1mvZjHHgG3JuQ6\" width=\"23\" height=\"21\"> are the standard deviations of these series.<\/p>\n\n\n\n<p>Alternate formula-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/wtddRnd0w3GvdmS4YF1TRq6MiK-IXXWAo3XMWMnGJ8Qci3ZpZw1Oa67OMVoFKlln47qYUQJYu7suHBnJRI10ceakWLm_6QKP-2kGGQ4GwD2BSlDYhIV0swACG3lXiOQrUHCYCREJ\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Note-<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li> Correlation coefficient always lies between -1 and +1.<\/li>\n\n\n\n<li> Correlation coefficient is independent of change of origin and scale.<\/li>\n\n\n\n<li> If the two variables are independent then correlation coefficient between them is zero.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Value of  (r)<\/strong><\/td><td><strong>Type of correlation<\/strong><\/td><\/tr><tr><td>+1<\/td><td>Perfect positive correlation<\/td><\/tr><tr><td>-1<\/td><td>Perfect negative correlation<\/td><\/tr><tr><td>0.25<\/td><td>Weak positive correlation<\/td><\/tr><tr><td>0.75<\/td><td>Strong positive correlation<\/td><\/tr><tr><td>-0.25<\/td><td>Weak negative correlation<\/td><\/tr><tr><td>-0.75<\/td><td>Strong negative correlation<\/td><\/tr><tr><td>0<\/td><td>No correlation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solved example<\/h2>\n\n\n\n<p><strong>Example: The data given below is about the marks obtained by a student and hours she studied.<\/strong><\/p>\n\n\n\n<p><strong>Find the correlation coefficient between hours and marks obtained.&nbsp; &nbsp; &nbsp; &nbsp; <\/strong><strong><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Hours<\/strong><\/td><td><strong>1<\/strong><\/td><td><strong>3<\/strong><\/td><td><strong>5<\/strong><\/td><td><strong>7<\/strong><\/td><td><strong>8<\/strong><\/td><td><strong>10<\/strong><\/td><\/tr><tr><td><strong>marks<\/strong><\/td><td><strong>8<\/strong><\/td><td><strong>12<\/strong><\/td><td><strong>15<\/strong><\/td><td><strong>17<\/strong><\/td><td><strong>18<\/strong><\/td><td><strong>20<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Let hours = x and marks = y<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/JvpxsmsFCPQpp7nHudUQaaPdhDcf3l1PSA8WGr1kK2TFLGnsgIrtPtS_DYlr0AynDyiKehk-pJ4aTIRVQgJsgCek3iWtGrJwv3zejlwltFCyqkhdeYDdtzLbKRf03vUtY334B-GX\" alt=\"\"\/><\/figure>\n\n\n\n<p>Karl Person\u2019s coefficient of correlation is given by-&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/duefLqzzkfYI1s0XmQ93kg0bcB2aBVNfVcKQGfDKoZPX-jjy2Th4BM0sngfgwWkHGvtbYUQwmeMBRyO608dCeHsUyB_unnfFZLNNNQ33-2kPQEZEh4fo9FBM9o-9qMR_PWiO8Omg\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>The correlation coefficient between hours and marks obtained is-<\/p>\n\n\n\n<p class=\"has-text-align-center\">r = 0.98<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Learn more about Correlation from here: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Correlation\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/en.wikipedia.org\/wiki\/Correlation<\/a><\/p>\n\n\n\n<p>Read more <a href=\"https:\/\/www.goseeko.com\/blog\/what-is-the-difference-between-primary-market-and-secondary-market\/\">Blogs here. <\/a> <a href=\"https:\/\/ceh.phfi.org\/\">https:\/\/ceh.phfi.org\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Basically correlation is the measurement of the strength of a linear relationship between two variables say x and y.<\/p>\n","protected":false},"author":3,"featured_media":2992,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-6473","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is Correlation? 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