Question

the table and scatter plot show the time spent watching tv, x, and the time spent doing homework, y, by each of 10 students last week. the equation of the line of best fit is $y = -0.2x + 19.63$. \

$$\begin{tabular}{|c|c|} \\hline time spent watching tv, x (in hours) & time spent doing homework, y (in hours) \\\\ \\hline 6.2 & 19.46 \\\\ \\hline 6.6 & 16.44 \\\\ \\hline 8.3 & 21.10 \\\\ \\hline 10.5 & 15.56 \\\\ \\hline 10.6 & 19.06 \\\\ \\hline 12.0 & 13.00 \\\\ \\hline 13.5 & 13.40 \\\\ \\hline 15.0 & 16.42 \\\\ \\hline 16.4 & 16.32 \\\\ \\hline 17.9 & 17.50 \\\\ \\hline \\end{tabular}$$

(scatter plot: x - axis time spent watching tv (in hours), y - axis time spent doing homework (in hours), with data points plotted) use the equation of the line of best fit to fill in the blanks below. give exact answers, not rounded approximations. \

$$\begin{tabular}{|c|c|c|c|} \\hline time spent watching tv (in hours) & observed time spent doing homework (in hours) & predicted time spent doing homework (in hours) & residual (in hours) \\\\ \\hline 12.0 & \\square & \\square & \\square \\\\ \\hline 17.9 & \\square & \\square & \\square \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Get observed y for x=12.0

From the first table, when $x=12.0$, observed $y=13.00$.

Step2: Calculate predicted y for x=12.0

Substitute $x=12.0$ into $y=-0.2x+19.63$:
$y=-0.2(12.0)+19.63 = -2.4 + 19.63 = 17.23$

Step3: Calculate residual for x=12.0

Residual = Observed - Predicted:
$13.00 - 17.23 = -4.23$

Step4: Get observed y for x=17.9

From the first table, when $x=17.9$, observed $y=17.50$.

Step5: Calculate predicted y for x=17.9

Substitute $x=17.9$ into $y=-0.2x+19.63$:
$y=-0.2(17.9)+19.63 = -3.58 + 19.63 = 16.05$

Step6: Calculate residual for x=17.9

Residual = Observed - Predicted:
$17.50 - 16.05 = 1.45$

Answer:

Time spent watching TV (in hours)	Observed time spent doing homework (in hours)	Predicted time spent doing homework (in hours)	Residual (in hours)
17.9	17.50	16.05	1.45