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Read the following description of a data set.\newlineMr. Carter is trying to convince his middle school typing students that it is better to slow down when they are learning to type. He argues that students who type too quickly make too many errors.To prove his point, Mr. Carter has students type a sample paragraph. He records their average typing speed (in words per minute), xx, and the number of errors they made, yy.The least squares regression line of this data set is:y=0.138x+10.252y = 0.138x + 10.252\newlineComplete the following sentence:\newlineFor an increase of one word per minute in typing speed, the least squares regression line predicts an increase of ___ errors while typing the sample paragraph.

Full solution

Q. Read the following description of a data set.\newlineMr. Carter is trying to convince his middle school typing students that it is better to slow down when they are learning to type. He argues that students who type too quickly make too many errors.To prove his point, Mr. Carter has students type a sample paragraph. He records their average typing speed (in words per minute), xx, and the number of errors they made, yy.The least squares regression line of this data set is:y=0.138x+10.252y = 0.138x + 10.252\newlineComplete the following sentence:\newlineFor an increase of one word per minute in typing speed, the least squares regression line predicts an increase of ___ errors while typing the sample paragraph.
  1. Identify Slope: Identify the slope of the least squares regression line. The equation given is y=0.138x+10.252y = 0.138x + 10.252. The slope of the least squares regression line is the coefficient of xx, which is 0.1380.138. This slope indicates the change in the number of errors, yy, for each one word per minute increase in typing speed, xx.
  2. Interpret Slope: Interpret the slope.\newlineSince the slope is 0.1380.138, this means that for each additional word per minute in typing speed, the least squares regression line predicts an increase of 0.1380.138 errors.

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