A researcher wants to investigate the relationship between the hours a student spends studying for a test and the score on the test. The following data is gathered: Hours (x) 20 16 34 23 27 32 18 22 Score (y) 6.5 8.5 7 9.5 7.5 (X-X)(Y-F) | (x-X)? Annual (X-X) salary, $1000 Years of (Y-Ÿ) (Y-F)² schooling 20 6.5 -4 -1.25 5 16 1.5625 16 6. -8 -1.75 14 64 3.0625 34 8.5 10 0.75 7.5 100 0.5625 23 7 -1 -0.75 0.75 1 0.5625 27 9 3 1.25 3.75 9. 1.5625 32 9.5 8. 1.75 14 64 3.0625 7.5 -6 -0.25 1.5 36 0.0625 22 8 -2 0.25 -0.5 4 0.0625 192 62 46 294 10.5 Calculate: a. The regression line of y based on x. b. The estimated test score for a person who studied 28 hours. m NN 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 2E
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A researcher wants to investigate the relationship between the hours a student spends studying for
a test and the score on the test. The following data is gathered:
Hours (x)
20
16
34
23
27
32
18
22
Score (y)
6.5
8.5
7
9.5
7.5
8
Annual (X-X)
salary,
$1000
Years of
(Y-Y)
(X-X)(Y-Ÿ)
(X-X)?
(Y-7)²
schooling
20
6.5
-4
-1.25
16
1.5625
16
6.
-8
-1.75
14
64
3.0625
34
8.5
10
0.75
7.5
100
0.5625
23
7
-1
-0.75
0.75
1
0.5625
27
3
1.25
3.75
9.
1.5625
32
9.5
8.
1.75
14
64
3.0625
18
7.5
-6
-0.25
1.5
36
0.0625
22
8
-2
0.25
-0.5
4
0.0625
192
62
46
294
10.5
Calculate:
a. The regression line of y based on x.
b. The estimated test score for a person who studied 28 hours.
Transcribed Image Text:A researcher wants to investigate the relationship between the hours a student spends studying for a test and the score on the test. The following data is gathered: Hours (x) 20 16 34 23 27 32 18 22 Score (y) 6.5 8.5 7 9.5 7.5 8 Annual (X-X) salary, $1000 Years of (Y-Y) (X-X)(Y-Ÿ) (X-X)? (Y-7)² schooling 20 6.5 -4 -1.25 16 1.5625 16 6. -8 -1.75 14 64 3.0625 34 8.5 10 0.75 7.5 100 0.5625 23 7 -1 -0.75 0.75 1 0.5625 27 3 1.25 3.75 9. 1.5625 32 9.5 8. 1.75 14 64 3.0625 18 7.5 -6 -0.25 1.5 36 0.0625 22 8 -2 0.25 -0.5 4 0.0625 192 62 46 294 10.5 Calculate: a. The regression line of y based on x. b. The estimated test score for a person who studied 28 hours.
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