Question

the scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 23 students. use the equation of the line of best fit, y = 1.82x + 11.36, to answer the questions below. give exact answers, not rounded approximations. (a) for an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment? (b) what is the predicted amount of money spent on entertainment for a student who doesnt work any hours? (c) what is the predicted amount of money spent on entertainment for a student who works 8 hours?

Explanation:

Step1: Analyze slope for part (a)

The equation of the line is $y = 1.82x+11.36$. The slope of the line is $1.82$. In a linear - regression equation $y = mx + b$, the slope $m$ represents the change in $y$ for a unit change in $x$. So for an increase of one hour in time worked ($x$), the predicted increase in the amount of money spent on entertainment ($y$) is given by the slope.

Step2: Find $y$ - intercept for part (b)

When a student doesn't work any hours, $x = 0$. Substitute $x = 0$ into the equation $y=1.82x + 11.36$. Then $y=1.82\times0 + 11.36=11.36$.

Step3: Substitute $x = 8$ for part (c)

Substitute $x = 8$ into the equation $y = 1.82x+11.36$. So $y=1.82\times8 + 11.36=14.56+11.36 = 25.92$.

Answer:

(a) $\$1.82$
(b) $\$11.36$
(c) $\$25.92$