A regression was run to determine if there is a relationship between hours of TV watched per day [tex]$(x)$[/tex] and number of situps a person can do [tex]$(y)$[/tex].
The results of the regression were:
[tex]
\begin{array}{l}
y=a x+b \
a=-1.34 \
b=36.954 \
r^2=0.966289 \
r=-0.983
\end{array}
[/tex]
Use this to predict the number of situps a person who watches 5 hours of TV can do (to one decimal place).
Answer (2)
Substitute x = 5 into the regression equation y = − 1.34 x + 36.954 .
Calculate y = ( − 1.34 ) ( 5 ) + 36.954 = − 6.7 + 36.954 = 30.254 .
Round the result to one decimal place: 30.3 .
The predicted number of situps is 30.3 .
Explanation
Understanding the Problem We are given a regression equation that relates the number of hours of TV watched per day ( x ) to the number of situps a person can do ( y ). The equation is y = a x + b , where a = − 1.34 and b = 36.954 . We want to predict the number of situps a person who watches 5 hours of TV can do.
Substituting the Value of x To predict the number of situps, we substitute x = 5 into the regression equation: y = ( − 1.34 ) ( 5 ) + 36.954
Calculating the Value of y Now, we calculate the value of y :
y = − 6.7 + 36.954 = 30.254
Rounding the Result We are asked to round the result to one decimal place. Therefore, the predicted number of situps is 30.3 .
Final Answer Therefore, a person who watches 5 hours of TV per day is predicted to be able to do 30.3 situps.
Examples
Understanding the relationship between lifestyle choices and physical fitness is crucial for maintaining a healthy life. For example, if a fitness app uses a similar regression model to predict sit-up performance based on daily TV watching habits, users can see how reducing screen time might positively impact their fitness levels. This encourages informed decisions about balancing leisure with exercise, promoting better health outcomes. By quantifying these relationships, individuals can set realistic fitness goals and track their progress effectively.
By substituting 5 into the regression equation y = − 1.34 x + 36.954 , we calculate y ≈ 30.3 after rounding. This means a person who watches 5 hours of TV is predicted to do around 30.3 situps. The final prediction helps illustrate the negative impact of excessive TV watching on physical fitness.
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