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.

Number of absences, x	Final grade, y
0	88.5
1	85.6
2	82.5
3	79.9
4	76.9
5	72.4
6	62.6
7	67.1
8	64.1
9	61.1

​(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.

y= x+

(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 unit change in the final​ grade, the number of days absent falls by ​days, on average.

B.For every day​ absent, the final grade falls by on average.

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

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

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

B.For every unit change in the final​ grade, the number of days absent falls by days, on average.

C.For every day​ absent, the final grade falls by on average.

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

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

​(c) Predict the final grade for a student who misses five 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 .This observation has a residual of which indicates that the final grade is average.

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

​(d) 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.Yes—15 missed class periods is possible and within the scope of the model

B.No—15 missed class periods is not possible.

C.No—15 missed class periods is outside the scope of the model.Your answer is correct.

D.No—15 missed class periods is not possible and outside the scope of the model.

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

2,

Square Footage, x	Selling Price ($000s), y
2254	387.5
3091	362
1131	190.4
2061	351.5
3021	607.7
2672	355
4123	629.6
2121	363
2525	411.9
1654	289.8
1780	270
3779	684.8

​(e) Find the​ least-squares regression line treating square footage as the explanatory variable.

y= x+( )

Answer 1

(1)

From the given data, the following Table is calculated:

X	Y	XY	X2
0	88.5	0	0
1	85.6	85.6	1
2	82.5	165.0	4
3	79.9	239.7	9
4	72.4	307.6	16
5	62.6	362.0	25
6	67.1	375.6	36
7	67.1	469.7	49
8	64.1	512.8	64
9	61.1	549.9	81
Total = 45	740.7	3067.9	285

Intercept (a) is given by:

Slope (b) is given by:

The Least Square Regression Line is given by:

(b)

(i)

Correct option:

B.     For every day​ absent, the final grade falls by on average. 3.215

(ii)

C.    For zero days​ absent, the final score is predicted to be 88.538

D.    For a final score of​ zero, the number of days absent is predicted to be days. = 88.538/3.215 = 27.5390 = 28 (Round to integer)

(c)

For x = 5:

Residual = 72.4 - 72.5 = - 0.1, So, below average

So,

Answer is:

The predicted final grade is 72.5 .This observation has a residual of which indicates that the final grade is below average.

(d)

Correct option:

C.       No—15 missed class periods is outside the scope of the model.

AS PER DIRECTIONS FOR ANSWERING, FIRST FULL QUESTION IS ANSWERED.