In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how man

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In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how man

y text messages they sent per day. The researcher decided to make the number of parties attended per week the explanatory variable and the number of text messages sent per day the response variable. The least squares regression line for this relationship is y-hat = 64.96 + 25.41x. One student attended 2 parties that week and sent 20 text messages per day. What is the residual?

Mathematics

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Svet_ta [9.5K] · Answer 1 · 2026-03-24T19:50:53+03:00

Answer: -95.78. Step-by-step explanation: The researcher classified the weekly party attendance as the explanatory variable, denoted as variable x in the regression equation, whereas the count of daily text messages sent, constitutes variable y. After formulating the linear regression equation, the researcher discovered that an estimated value for the actual 'y' could be represented by the resulting line. It should be noted that, as it’s an estimate, it’s not anticipated to align precisely with the actual value of 'y'. Hence, we define the residual for each x value as the difference between the actual and the estimated 'y' values. For the recorded 'x' value of 2 (the student attending 2 parties), the actual 'y' value is 20 (the student sent 20 text messages per day). According to the regression line, the approximated 'y' value would be derived.