The scatter plot shows the time spent watching TV, x, and the time spent doing h

Question

The scatter plot shows the time spent watching TV, x, and the time spent doing homework, y, by each of 24 students last week. 28 Time spent doing homework (in hours) 412 1620 24 32 Time spant watching TV (in hours) Use the equation of the line of best fit, y -0.77x 26.08, to answer the questions below. Give exact answers, not rounded approximations. (a) What is the predicted time spent doing homework for a student who doesn't spend any time watching TV? (b) What is the predicted time spent doing homework for a student who spends 12 hours watching TV? hours (c) For an increase of one hour in the time spent watching TV, what is the predicted decrease in the time spent doing homework? hours

Explanation / Answer

The line of best fit is y = -0.77x+26.08

(a). If a student does not spend any time watching TV, then x = 0 so that y = 26.08. However, a day has 24 hours only so that y has to be less than or equal to 24. Hence the time spent on doing home work is 24 hours.

(b). If x = 12, then y = -0.77*12 + 26.08 = -9.24+26.08 = 16.84. Thus, the time spent on doing home work is 16.84 hours.

( c). The coefficient of x is -0.77 so that if we increase x by 1, then y will decrease by 0.77. Thus, the time spent on doing home workwill decrease by 0.77 hour.

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