Question

the table and scatter plot show the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 10 students. the equation of the line of best fit is y = 0.4x + 23.62. number of hours worked, x amount spent on entertainment, y (in dollars) 3.9 22.57 4.4 27.82 5.6 20.09 7.0 23.37 7.0 28.82 8.1 33.50 9.1 33.50 9.9 26.35 10.9 25.34 12.2 25.00 use the equation of the line of best fit to fill in the blanks below. give exact answers, not rounded approximations. number of hours worked observed amount spent on entertainment (in dollars) predicted amount spent on entertainment (in dollars) residual (in dollars) 8.1 12.2

Explanation:

Step1: Get observed values

From the first table:
For $x=8.1$, observed $y=33.50$
For $x=12.2$, observed $y=25.00$

Step2: Calculate predicted values

Use $\hat{y}=0.4x + 23.62$:
For $x=8.1$:
$\hat{y}=0.4(8.1)+23.62=3.24+23.62=26.86$
For $x=12.2$:
$\hat{y}=0.4(12.2)+23.62=4.88+23.62=28.50$

Step3: Calculate residuals

Residual = Observed $y$ - Predicted $\hat{y}$:
For $x=8.1$:
$33.50 - 26.86=6.64$
For $x=12.2$:
$25.00 - 28.50=-3.50$

Answer:

Number of hours worked	Observed amount spent on entertainment (in dollars)	Predicted amount spent on entertainment (in dollars)	Residual (in dollars)
12.2	25.00	28.50	-3.50