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. hours
linear regression
$y \approx 1.62x + 0.117; r \approx 0.92$
$0.14995 \leq x \leq 4.35$
$0.39995 \leq y \leq 7.6$

Explanation:

Step1: Identify the variables

We have the regression equation $y = 1.62x+ 0.117$, where $y$ is the level and $x$ is the number of hours. We want to find $x$ when $y = 5$.

Step2: Rearrange the equation

Substitute $y = 5$ into the equation $5=1.62x + 0.117$. Then, subtract $0.117$ from both sides: $5 - 0.117=1.62x$, so $4.883 = 1.62x$.

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:

$3.0$