Reading is fundamental to a teenager's ability to perform well in school. Assume a researcher isinterested in the ability of the number of books read over the summer to predict ACT Readingscores. Using a random sample of 10 random high school students the researchers recorded thenumber of books read over the summer and the students' ACT Reading scores.Books Read (X) ACT Score (Y) (X- Xmean)(Y - Ymean)(X-Xmean)(Y-Ymean) (X-Xmean)?(Y - Ymean)?216-5.4-14.98129221219-5.4-11.96429141317-4.4-13.96120192425-3.4-5.920123421-3.4-9.934129724-1.4-6.910247621-1.4-9.9142978240.6-6.9-447727-0.4-3.921510222.6-8.9-23778Total52216259.1113.3969.3МEAN7.430.9a. Identify the regression line using the number of books read to predict ACT Readingscore. Use a = .05 to evaluate the quality of the prediction of the regression line.b. What is the predicted ACT Reading score when 5 books are read?

X Y (x-xbar) (x-xbar)^2 (y-ybar) (y-ybar)^2 (x-xbar)*(y-ybar) ypred Residual Resiudal^2 2 16 -3.2…

Answered: a. Identify the regression line using…

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Reading is fundamental to a teenager's ability to perform well in school. Assume a researcher is
interested in the ability of the number of books read over the summer to predict ACT Reading
scores. Using a random sample of 10 random high school students the researchers recorded the
number of books read over the summer and the students' ACT Reading scores.
Books Read (X) ACT Score (Y) (X- Xmean)
(Y - Ymean)
(X-Xmean)(Y-Ymean) (X-Xmean)?
(Y - Ymean)?
2
16
-5.4
-14.9
81
29
221
2
19
-5.4
-11.9
64
29
141
3
17
-4.4
-13.9
61
20
192
4
25
-3.4
-5.9
20
12
34
21
-3.4
-9.9
34
12
97
24
-1.4
-6.9
10
2
47
6
21
-1.4
-9.9
14
2
97
8
24
0.6
-6.9
-4
47
7
27
-0.4
-3.9
2
15
10
22
2.6
-8.9
-23
7
78
Total
52
216
259.1
113.3
969.3
МEAN
7.4
30.9
a. Identify the regression line using the number of books read to predict ACT Reading
score. Use a = .05 to evaluate the quality of the prediction of the regression line.
b. What is the predicted ACT Reading score when 5 books are read?

Expert Solution

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X	Y	(x-xbar)	(x-xbar)^2	(y-ybar)	(y-ybar)^2	(x-xbar)*(y-ybar)	ypred	Residual	Resiudal^2
2	16	-3.2	10.24	-5.6	31.36	17.92	18.94	-2.94	8.66
2	19	-3.2	10.24	-2.6	6.76	8.32	18.94	0.06	0.00
3	17	-2.2	4.84	-4.6	21.16	10.12	19.77	-2.77	7.69
4	25	-1.2	1.44	3.4	11.56	-4.08	20.60	4.40	19.33
4	21	-1.2	1.44	-0.6	0.36	0.72	20.60	0.40	0.16
6	24	0.8	0.64	2.4	5.76	1.92	22.26	1.74	3.01
6	21	0.8	0.64	-0.6	0.36	-0.48	22.26	-1.26	1.60
8	24	2.8	7.84	2.4	5.76	6.72	23.92	0.08	0.01
7	27	1.8	3.24	5.4	29.16	9.72	23.09	3.91	15.25
10	22	4.8	23.04	0.4	0.16	1.92	25.58	-3.58	12.85

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