Question

Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. A line was fit to the data to model the relationship.Which of these linear equations best describes the given model?A) ŷ = 5x + 1.5B) ŷ = 1.5x + 5Or C) ŷ = -1.5x + 5Based on this equation, estimate the mood rating for a student that spent 2.5 hours playing sports.Round your answer to the nearest hundredth.__________.

Answer 1

We have to relate a linear function (the regression model) with its equation.

We can see in the graph that the y-intercept, the value of y(0), is b=5.

Then, we can estimate the slope with the known points (0,5) and (2,8):

`m=(y_2-y_1)/(x_2-x_1)=(8-5)/(2-0)=(3)/(2)=1.5`

Then, with slope m=1.5 and b=5, the regression model equation should be:

`y=1.5x+5`

We can estimate the mood for students that spent 2.5 hours playing sports by replacing x with 2.5 in the model and calculate y:

`y(2.5)=1.5\cdot2.5+5=3.75+5=8.75`

NOTE: we could also have look on the graph instead of doing the calculation.

Answer: B) y=1.5x+5

The estimation of the mood for a student that spent 2.5 hours playing sports is 8.75.