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Read the following description of a data set. Walter thinks that text messaging is causing him to talk less on the phone. For one month, he examined his text message and call logs with his closest friends.For each friend, Walter checked the number of text messages he sent to that friend, xx, and the number of minutes they spoke on the phone, yy.The least squares regression line of this data set is: y=2.336x+856.039y = -2.336x + 856.039 \newlineComplete the following sentence:\newline If Walter sent one more text message to a friend, the least squares regression line predicts he would have spent __\_\_ fewer minutes on the phone with them.

Full solution

Q. Read the following description of a data set. Walter thinks that text messaging is causing him to talk less on the phone. For one month, he examined his text message and call logs with his closest friends.For each friend, Walter checked the number of text messages he sent to that friend, xx, and the number of minutes they spoke on the phone, yy.The least squares regression line of this data set is: y=2.336x+856.039y = -2.336x + 856.039 \newlineComplete the following sentence:\newline If Walter sent one more text message to a friend, the least squares regression line predicts he would have spent __\_\_ fewer minutes on the phone with them.
  1. Identify the slope: Identify the slope of the least squares regression line.\newlineThe equation given is y=2.336x+856.039y = -2.336x + 856.039. The slope of the least squares regression line is the coefficient of xx, which is 2.336-2.336. This slope indicates the change in the number of minutes on the phone (yy) for each additional text message sent (xx).
  2. Interpret the slope: Interpret the slope.\newlineSince the slope is 2.336-2.336, this means that for each additional text message sent, the number of minutes spent on the phone decreases by 2.3362.336 minutes. This is because the slope represents the rate of change in yy for each one-unit increase in xx.
  3. Apply the slope: Apply the slope to the scenario of sending one more text message. If Walter sends one more text message, the least squares regression line predicts that he would spend 2.3362.336 fewer minutes on the phone with that friend.

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