Problem

A regression was run to determine if there is a relationship between hours of TV watched per day $(x)$ and number of situps a person can do $(y)$. The results of the regression were: \[ \begin{array}{l} y=a x+b \\ a=-1.082 \\ b=32.931 \\ r^{2}=0.5625 \\ r=-0.75 \end{array} \] Use this to predict the number of situps a person who watches 7.5 hour(s) of TV can do, and please round your answer to a whole number.

Solution

Step 1 :The problem provides a regression equation in the form \(y = ax + b\), where \(y\) is the number of situps a person can do, \(x\) is the number of hours of TV watched, \(a\) is the slope of the line, and \(b\) is the y-intercept.

Step 2 :The given values are \(a = -1.082\), \(b = 32.931\), and \(x = 7.5\).

Step 3 :To predict the number of situps for a person who watches 7.5 hours of TV, we substitute \(x = 7.5\) into the equation and solve for \(y\).

Step 4 :Substituting the values into the equation gives \(y = -1.082 * 7.5 + 32.931\).

Step 5 :Solving the equation gives \(y = 25\).

Step 6 :Final Answer: The predicted number of situps a person who watches 7.5 hours of TV can do is \(\boxed{25}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17665/

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