{"id":48551,"date":"2024-04-15T22:42:55","date_gmt":"2024-04-15T22:42:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=48551"},"modified":"2024-04-15T22:42:55","modified_gmt":"2024-04-15T22:42:55","slug":"which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","title":{"rendered":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9801e84d9e9\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    1, 2 and 3                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    1,3 and 4                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    1 and 3                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"true\">\r\n                    All of above                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is D. All of the above.<\/p>\n<p>The assumptions of linear regression are:<\/p>\n<ol>\n<li>The true relationship between dependent $y$ and predictor $x$ is linear. This means that the line of best fit is the best way to represent the data.<\/li>\n<li>The model errors are statistically independent. This means that the errors are not correlated with each other.<\/li>\n<li>The errors are normally distributed with a 0 mean and constant standard deviation. This means that the errors are evenly distributed around the line of best fit, with a mean of 0 and a constant standard deviation.<\/li>\n<li>The predictor $x$ is non-stochastic and is measured error-free. This means that the predictor is not random and is measured without error.<\/li>\n<\/ol>\n<p>If any of these assumptions are violated, the results of the linear regression may not be accurate. For example, if the true relationship between $y$ and $x$ is not linear, the line of best fit will not be the best way to represent the data. If the errors are correlated with each other, the standard errors of the coefficients will be underestimated. <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> If the errors are not normally distributed, the t-tests and F-tests may not be accurate. If the predictor $x$ is random or is measured with error, the coefficients will be biased.<\/p>\n<p>It is important to check the assumptions of linear regression before using the results. There are a number of ways to do this, including looking at the residuals, the normality plot, and the Cook&#8217;s distance. If any of the assumptions are violated, you may need to transform the data or use a different statistical method.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free\" \/>\n<meta property=\"og:description\" content=\"Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T22:42:55+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","og_locale":"en_US","og_type":"article","og_title":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free","og_description":"Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T22:42:55+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","name":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T22:42:55+00:00","dateModified":"2024-04-15T22:42:55+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Machine learning","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/machine-learning\/"},{"@type":"ListItem","position":4,"name":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/48551"}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=48551"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/48551\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=48551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=48551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=48551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}