Chapter PII, Problem 12RE

(a)

To determine

To find out what is the correlation between Friday and Monday scores.

Answer to Problem 12RE

The correlation between the scores of Monday and Friday is $0.473$ .

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question as:

Friday	Monday
42	36
44	44
45	46
48	38
44	40
43	38
41	37
35	31
43	32
48	37
43	41
45	32
47	44
50	47
34	34
38	31
43	40
39	41
46	32
37	36
40	31
41	32
48	39
37	31
36	41

Thus, to find the correlation between the scores of Monday and Friday we will use the Excel function, that is,

  $=\text{CORREL}(\text{array1, array2})$

Thus, the result will be as:

Correlation=

=CORREL(Q45:Q69,R45:R69)

Correlation=

0.473

Thus, the correlation between the scores of Monday and Friday is $0.473$ .

(b)

To determine

To find out what does a scatterplot show about the association between the scores.

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question. Thus, the scatterplot show about the association between the scores that the better they got on Friday they would also probably have a higher score on Monday too. The scatterplot is as follows:

  

(c)

To determine

To find out what does it mean for a student to have a positive residual.

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question. Thus, for a student to have a positive residual means that the student did better on Monday test than predicted by the model.

(d)

To determine

To explain what would you predict about a student whose Friday score was one standard deviation below average.

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question. Thus, we predict about a student whose Friday score was one standard deviation below average that they would probably have a Monday score one standard deviation below average.

(e)

To determine

To write the equation of the regression line.

Answer to Problem 12RE

   .

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question. Thus, to find the equation of the regression line we will select the data in Excel and then go to the insert tab and select the scatterplot from it. Then when the scatterplot is plotted we will go to the quick layout option to select the layout of the equation line and the regression line will appear on the scatterplot as:

  

Thus, the regression line is as:

  

(f)

To determine

To predict the Monday score of a student who earned a $40$ on Friday.

Answer to Problem 12RE

The Monday score is $36.02$ .

Explanation of Solution

It is given in the question that researchers gave students enrolled in a section of basic Spanish a set of vocabulary words to memorize. Thus, the tests were conducted on Monday and Friday and the scores are given in the table given in the question. And the regression line is as:

  

Thus, to predict the Monday score of a student who earned a $40$ on Friday as: