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  Inference for Regression
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<h3 id="Inference-for-Regression">Inference for Regression<a class="anchor-link" href="#Inference-for-Regression"> </a></h3><p>Thus far, our analysis of the relation between variables has been purely descriptive. We know how to find the best straight line to draw through a scatter plot. The line is the best in the sense that it has the smallest mean squared error of estimation among all straight lines.</p>
<p>But what if our data were only a sample from a larger population? If in the sample we found a linear relation between the two variables, would the same be true for the population? Would it be exactly the same linear relation? Could we predict the response of a new individual who is not in our sample?</p>
<p>Such questions of inference and prediction arise if we believe that a scatter plot reflects the underlying relation between the two variables being plotted but does not specify the relation completely. For example, a scatter plot of birth weight versus gestational days shows us the precise relation between the two variables in our sample; but we might wonder whether that relation holds true, or almost true, for all babies in the population from which the sample was drawn, or indeed among babies in general.</p>
<p>As always, inferential thinking begins with a careful examination of the assumptions about the data. Sets of assumptions are known as <em>models</em>. Sets of assumptions about randomness in roughly linear scatter plots are called <em>regression models</em>.</p>

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