Question

devin recorded the number of hours he played a video game, x, and the levels he achieved, y. the regression calculator shows the equation for the line of best fit. use the equation to interpolate the values and estimate the time it would take him to get to level 5. round to the nearest half hour. linear regression y ≈ 1.62x + 0.117; r ≈ 0.92 0.14999 ≤ x ≤ 4.35 0.39999 ≤ y ≤ 7.6

Explanation:

Step1: Set up the equation

We are given the regression equation $y = 1.62x+0.117$ and we want to find $x$ when $y = 5$. So we set up the equation $5=1.62x + 0.117$.

Step2: Isolate the variable term

Subtract $0.117$ from both sides of the equation: $5 - 0.117=1.62x$, which simplifies to $4.883 = 1.62x$.

Step3: Solve for $x$

Divide both sides by $1.62$: $x=\frac{4.883}{1.62}\approx3.014$.

Step4: Round to the nearest half - hour

Rounding $3.014$ to the nearest half - hour gives $3.0$ hours.

Answer:

$3.0$