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 &bull;
 <div class="font-base text-sm"> <time datetime="2024-11-07T00:00:00.000Z"> November 07, 2024 </time> </div> 
 &bull;
+<div class="font-base text-sm">
+Last modified:  <time datetime="2024-11-07T07:44:29.000Z"> November 07, 2024 </time> </div> 
+&bull;
 <div class="font-base text-sm"> 10 min read </div> </div> <h1 class="animate text-3xl font-semibold text-black dark:text-white"> Part 4 - Simple Linear Regression </h1> </div> <details open class="animate rounded-lg border border-black/15 dark:border-white/20" data-astro-cid-xvrfupwn> <summary data-astro-cid-xvrfupwn>Table of Contents</summary> <nav class="" data-astro-cid-xvrfupwn> <ul class="py-3" data-astro-cid-xvrfupwn> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#introduction" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Introduction </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#simple-linear-regression" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Simple Linear Regression </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#least-squares-estimator" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Least Squares Estimator </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#inferences" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Inferences </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#confidence-interval" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Confidence Interval </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#confidence-interval-on-the-mean-response" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Confidence Interval on the Mean Response </a>  </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#prediction-of-new-observations" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Prediction of new observations </a>  </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#analysis-of-variance-anova" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Analysis of Variance (ANOVA) </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#analysis-of-variance-table" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Analysis of Variance Table </a>  </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#coefficient-of-determination" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Coefficient of Determination </a> <ul class="translate-x-3"> <li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#connection-to-correlation-coefficient" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Connection to correlation coefficient </a>  </li> </ul> </li> </ul> </li><li class="list-inside list-disc px-6 py-1.5 text-sm"> <a href="#example" target="_self" class="inline-block decoration-black/30 dark:decoration-white/30 hover:decoration-black/50 focus-visible:decoration-black/50 dark:hover:decoration-white/50 dark:focus-visible:decoration-white/50 text-current hover:text-black focus-visible:text-black dark:hover:text-white dark:focus-visible:text-white transition-colors duration-300 ease-in-out underline underline-offset-[3px]"> Example </a>  </li> </ul> </nav> </details> <article class="animate"> <h3 id="introduction">Introduction</h3>
 <p>The main objective of many statistical investigations is to make predictions.</p>
 <p>For instance, an engineer may wish to predict the amount of oxide that will form on the surface of a metal baked in an oven for one hour at 200$^{\circ}$C, or the amount of deformation of a ring subjected to a certain compressive force.</p>

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