Question

a gym franchise was considering a television marketing campaign to increase its membership. the franchises market researchers wanted to get a better sense of the television and exercise habits of the gyms target demographic. to begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month. using the survey responses, the researchers compared the number of hours of television watched, x, to the number of hours of exercise, y, for each member. the least - squares regression line of this data set is: y = - 2.137x + 61.966. how many hours of exercise does this line predict for a gym member who watched 6.86 hours of television last month? round your answer to the nearest thousandth.

Explanation:

Step1: Identify the regression equation

The regression equation is $y = - 2.137x+61.966$, where $x$ is the number of hours of television watched and $y$ is the number of hours of exercise.

Step2: Substitute the given value of $x$

We are given $x = 6.86$. Substitute $x = 6.86$ into the equation:
$y=-2.137\times6.86 + 61.966$.

Step3: Calculate the value of $y$

First, calculate $-2.137\times6.86=-2.137\times(6 + 0.86)=-2.137\times6-2.137\times0.86=-12.822-1.83782=-14.65982$.
Then, $y=-14.65982 + 61.966=47.30618$.

Step4: Round the answer

Rounding $47.30618$ to the nearest thousandth, we get $y = 47.306$.

Answer:

$47.306$