Chapter2.3 - 2.3 Least Squares Regression If a scatterplot...

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2.3 Least Squares Regression If a scatterplot shows a linear relationship which is moderately strong as measured by the correlation, we would like to draw a line on the scatterplot to summarize the relationship. In the case where there is a response and an explanatory variable, the least-squares regression line often provides a good summary of this relationship. Regression Line The regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x. Regression, unlike correlation, requires that we have an explanatory variable and a response variable. Please look at Page 123 for Example 2.9
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Figure 2.11 Weight gain after 8 weeks of overeating, plotted against increase in nonexercise activity over the same period, for Example 2.9 Example How do children grow? The pattern of growth varies from child to child, so we can best understand the general pattern by following the average height of a number of children.
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Figure . Mean height of children in Kalama, Egypt, plotted against age from 18 to 29 months, from Table 2.7.
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Origins of Regression: “Regression Analysis was first developed by Sir Francis Galton in the latter part of the 19 th Century. Galton had studied the relation between heights of fathers and sons and noted that the heights of sons of both tall & short fathers appeared to ‘revert’ or ‘regress’ to the mean of the group. He considered this tendency to be a regression to ‘mediocrity.’ Galton developed a mathematical description of this tendency, the precursor to today’s regression models.” Straight Lines Suppose that y is a response variable (plotted on the vertical axis) and x is an explanatory
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Chapter2.3 - 2.3 Least Squares Regression If a scatterplot...

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