Question

the scatter - plot shows the time spent watching tv, x, and the time spent doing homework, y. use the equation of the line of best fit, y = - 0.78x + 26.12, to answer the questions below. give exact answers, not rounded approximations. (a) what is the predicted time spent doing homework for a student who doesnt spend any time watching tv? (b) for an increase of one hour in the time spent watching tv, what is the predicted decrease in the time spent doing homework? (c) what is the predicted time spent doing homework for a student who spends 15 hours watching tv?

Explanation:

Step1: Substitute \(x = 0\) into the equation

The equation is \(y=-0.78x + 26.12\). When \(x = 0\) (student doesn't spend any time watching TV), we have \(y=-0.78\times0+26.12\).

Step2: Calculate the value of \(y\)

\(y = 26.12\)

Step3: Analyze the coefficient of \(x\) for part (b)

The slope of the line \(y=-0.78x + 26.12\) is \(- 0.78\). This means for an increase of one - unit in \(x\) (one hour increase in time spent watching TV), the value of \(y\) (time spent doing homework) decreases by \(0.78\) hours.

Step4: Substitute \(x = 15\) into the equation for part (c)

Substitute \(x = 15\) into \(y=-0.78x + 26.12\), we get \(y=-0.78\times15+26.12\).
First, calculate \(-0.78\times15=-11.7\). Then \(y=-11.7 + 26.12=14.42\).

Answer:

(a) \(26.12\) hours
(b) \(0.78\) hours
(c) \(14.42\) hours