Question

the table and scatter plot show the time spent texting, x, and the time spent exercising, y, by each of 11 students last week. the equation of the line of best fit is $y = -0.5x + 7.56$. \

$$\begin{tabular}{|c|c|} \\hline time spent texting, x (in hours) & time spent exercising, y (in hours) \\\\ \\hline 1.5 & 7.48 \\\\ \\hline 2.1 & 6.55 \\\\ \\hline 2.3 & 5.40 \\\\ \\hline 2.8 & 6.93 \\\\ \\hline 3.6 & 5.19 \\\\ \\hline 4.1 & 5.51 \\\\ \\hline 4.6 & 5.30 \\\\ \\hline 5.0 & 6.50 \\\\ \\hline 5.4 & 6.02 \\\\ \\hline 5.5 & 3.31 \\\\ \\hline 6.0 & 4.47 \\\\ \\hline \\end{tabular}$$

(scatter plot: x - axis: time spent texting (in hours), y - axis: time spent exercising (in hours)) use the equation of the line of best fit to fill in the blanks below. give exact answers, not rounded approximations. \

$$\begin{tabular}{|c|c|c|c|} \\hline time spent texting (in hours) & observed time spent exercising (in hours) & predicted time spent exercising (in hours) & residual (in hours) \\\\ \\hline 4.1 & & & \\\\ \\hline 5.0 & & & \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Get observed values from table

For $x=4.1$, observed $y=5.51$; for $x=5.0$, observed $y=6.50$.

Step2: Calculate predicted values

For $x=4.1$:
$y = -0.5(4.1) + 7.56 = -2.05 + 7.56 = 5.51$
For $x=5.0$:
$y = -0.5(5.0) + 7.56 = -2.5 + 7.56 = 5.06$

Step3: Calculate residuals (observed - predicted)

For $x=4.1$:
$5.51 - 5.51 = 0$
For $x=5.0$:
$6.50 - 5.06 = 1.44$

Answer:

Time spent texting (in hours)	Observed time spent exercising (in hours)	Predicted time spent exercising (in hours)	Residual (in hours)
5.0	6.50	5.06	1.44