Question

The data below represent the number of days​ absent, x, and the final​ grade, y, for a sample of college students at a large university. Complete parts​ (a) through​ (e) below.

No. of​ absences, x	00	11	22	33	44	55	66	77	88	99
Final​ grade, y	88.188.1	85.285.2	82.282.2	79.879.8	76.876.8	72.372.3	62.862.8	67.267.2	64.364.3	61.461.4

​(a) Find the​ least-squares regression line treating the number of​ absences, x, as the explanatory variable and the final​ grade, y, as the response variable.

ModifyingAbove y with caretyequals=nothingxplus+left parenthesis nothing right parenthesis

​(Round to three decimal places as​ needed.)

​(b) Interpret the slope and​ y-intercept, if appropriate.

Interpret the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(Round to three decimal places as​ needed.)

A.For every day​ absent, the final grade

fallsfalls

by

nothing​,

on average.

B.For a final score of​ zero, the number of days absent is predicted to be

nothing

days.

C.For every unit change in the final​ grade, the number of days absent

fallsfalls

by

nothing

​days, on average.

D.For zero days​ absent, the final score is predicted to be

nothing.

E.

It is not appropriate to interpret the slope.

Interpret the​ y-intercept. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(Round to three decimal places as​ needed.)

A.For every unit change in the final​ grade, the number of days absent

fallsfalls

by

nothing

​days, on average.

B.For zero days​ absent, the final score is predicted to be

nothing.

C.For every day​ absent, the final grade

fallsfalls

by

nothing​,

on average.

D.For a final score of​ zero, the number of days absent is predicted to be

nothing

days.

E.

It is not appropriate to interpret the​ y-intercept.

​(c) Predict the final grade for a student who misses

fivefive

class periods and compute the residual. Is the observed final grade above or below average for this number of​ absences?The predicted final grade is

nothing.

This observation has a residual of

nothing​,

which indicates that the final grade is

▼

below

above

average.

​(Round to one decimal place as​ needed.)

​(d) Draw the​ least-squares regression line on the scatter diagram of the data. Choose the correct graph below.

A.

01050100xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 50 to 100 in increments of 5. The following ten points are plotted: (0,88.1), (1,85.2), (2,82.2), (3,79.8), (4,76.8), (5,72.3), (6,62.8), (7,67.2), (8,64.3), and (9,61.4). A line, decreasing from left to right, passes through the approximate points (0, 89.1) and (4, 77.2).

B.

01050100xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 50 to 100 in increments of 5. The following ten points are plotted: (0,88.1), (1,85.2), (2,82.2), (3,79.8), (4,76.8), (5,72.3), (6,62.8), (7,67.2), (8,64.3), and (9,61.4). A line, decreasing from left to right, passes through the approximate points (0, 90.6) and (4, 78.1).

C.

01050100xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 50 to 100 in increments of 5. The following ten points are plotted: (0,88.1), (1,85.2), (2,82.2), (3,79.8), (4,76.8), (5,72.3), (6,62.8), (7,67.2), (8,64.3), and (9,61.4). A line, decreasing from left to right, passes through the approximate points (0, 88.1) and (4, 75.6).

D.

01050100xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 50 to 100 in increments of 5. The following ten points are plotted: (0,88.1), (1,85.2), (2,82.2), (3,79.8), (4,76.8), (5,72.3), (6,62.8), (7,67.2), (8,64.3), and (9,61.4). A line, decreasing from left to right, passes through the approximate points (0, 87.1) and (4, 74.6).

​(e) Would it be reasonable to use the​ least-squares regression line to predict the final grade for a student who has missed 15 class​ periods? Why or why​ not?

A.

Nolong dash—15

missed class periods is not possible and outside the scope of the model.

B.

Yeslong dash—15

missed class periods is possible and within the scope of the model

C.

Nolong dash—15

missed class periods is outside the scope of the model.

D.

Nolong dash—15

missed class periods is not possible.

E.

More information regarding the student is necessary to be able to make a decision.

Click to select your answer(s).

Answer 1