Question

the table and scatter plot show the time spent texting, x, and the time spent exercising, y, by each of 10 students last week.
the equation of the line of best fit is ( y=-0.3x + 6.74 ).
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use the equation of the line of best fit to fill in the blanks below.
give exact answers, not rounded approximations.
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Explanation:

Step1: Find observed values

From the table, when \(x = 4.0\), the observed \(y\) (time spent exercising) is \(4.50\). When \(x=6.0\), the observed \(y\) is \(5.50\).

Step2: Calculate predicted values

For the line of best - fit \(y=-0.3x + 6.74\).
When \(x = 4.0\):
Substitute \(x = 4.0\) into \(y=-0.3x + 6.74\)
\(y=-0.3\times4.0+6.74=-1.2 + 6.74 = 5.54\)
When \(x = 6.0\):
Substitute \(x = 6.0\) into \(y=-0.3x + 6.74\)
\(y=-0.3\times6.0+6.74=-1.8+6.74 = 4.94\)

Step3: Calculate residuals

The formula for the residual is \(e=y_{observed}-y_{predicted}\)
When \(x = 4.0\):
\(e=4.50 - 5.54=-1.04\)
When \(x = 6.0\):
\(e=5.50 - 4.94 = 0.56\)

Answer:

Time spent texting (in hours)	Observed time spent exercising (in hours)	Predicted time spent exercising (in hours)	Residual (in hours)
\(6.0\)	\(5.50\)	\(4.94\)	\(0.56\)