Question

The accompanying data represent the number of days​ absent, x, and the final exam​ score, y, for a sample of college students in a general education course at a large state university. Complete parts ​(a) through​ (e) below.

Absences and Final Exam Scores

No. of absences, x	0	1	2	3	4	5	6	7	8	9
Final exam score, y	89.6	87.3	83.4	81.2	78.7	74.3	64.5	71.1	66.4	65.6

Critical Values for Correlation Coefficient

n
3	0.997
4	0.950
5	0.878
6	0.811
7	0.754
8	0.707
9	0.666
10	0.632
11	0.602
12	0.576

​

(a) Find the​ least-squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable.

y = __x + __

​(b) Interpret the slope and the​ y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice.​​​​​​​ ​(Round to three decimal places as​ needed.)

A. For every additional​ absence, a​ student's final exam score drops ___ points, on average. The average final exam score of students who miss no classes is ___.

B. For every additional​ absence, a​ student's final exam score drops ____ ​points, on average. It is not appropriate to interpret the​ y-intercept.

C. The average final exam score of students who miss no classes is ____. It is not appropriate to interpret the slope.

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

​(c) Predict the final exam score for a student who misses five class periods.

y = ___ (Round to two decimals places as needed.)

Compute the residual.

____ (Round to two decimal places as needed.)

Is the final exam score above or below average for this number of​ absences?​​​​​​​

A. Below

B. Above

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

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

A. ​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10.

B. ​Yes, because the purpose of finding the regression line is to make predictions outside the scope of the model.

C.​ No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n = 10.

D. ​No, because 15 absences is outside the scope of the model.

Answer 1

a)

y =-2.899*x +89.255

b)

A. For every additional​ absence, a​ student's final exam score drops 2.899 points, on average. The average final exam score of students who miss no classes is 89.255

c)

predicted val=89.255+5*-2.899=

74.76

residual =74.3-74.76= -0.46

A. Below
d)

e)

D. ​No, because 15 absences is outside the scope of the model.