An instructor asked a random sample of eight students to record their study times at the beginning of a course. She then made a table for total hours studied (x) over 2 weeks and test score (y) at the end of the 2 weeks. The table is given below. Complete parts (a) through (d). x 11 13 10 20 7 16 15 24 y 91 82 87 72 87 77 89 78 ∑x=116, ∑y=663, ∑xy=9,425, ∑x2=1,896 a. Compute SST, SSR, and SSE, using the formulas SST=∑y2i−∑yi2/n, SSR=∑xiyi−∑xi∑yi/n2∑x2i−∑xi2/n and SSE=SST−SSR. SST= (Round to two decimal places as needed.) SSR= (Round to two decimal places as needed.) SSE= (Round to two decimal places as needed.) b. Compute the coefficient of determination, r2= (Round to four decimal places as needed.) c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. _____________% (Round to two decimal places as needed.)
An instructor asked a random sample of eight students to record their study times at the beginning of a course. She then made a table for total hours studied (x) over 2 weeks and test score (y) at the end of the 2 weeks. The table is given below. Complete parts (a) through (d). x 11 13 10 20 7 16 15 24 y 91 82 87 72 87 77 89 78 ∑x=116, ∑y=663, ∑xy=9,425, ∑x2=1,896 a. Compute SST, SSR, and SSE, using the formulas SST=∑y2i−∑yi2/n, SSR=∑xiyi−∑xi∑yi/n2∑x2i−∑xi2/n and SSE=SST−SSR. SST= (Round to two decimal places as needed.) SSR= (Round to two decimal places as needed.) SSE= (Round to two decimal places as needed.) b. Compute the coefficient of determination, r2= (Round to four decimal places as needed.) c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. _____________% (Round to two decimal places as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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An instructor asked a random sample of eight students to record their study times at the beginning of a course. She then made a table for total hours studied (x) over 2 weeks and test score (y) at the end of the 2 weeks. The table is given below. Complete parts (a) through (d).
|
x
|
11
|
13
|
10
|
20
|
7
|
16
|
15
|
24
|
|
|---|---|---|---|---|---|---|---|---|---|
|
y
|
91
|
82
|
87
|
72
|
87
|
77
|
89
|
78
|
|
∑x=116, ∑y=663, ∑xy=9,425, ∑x2=1,896
a. Compute SST, SSR, and SSE, using the formulas
SST=∑y2i−∑yi2/n,
SSR=∑xiyi−∑xi∑yi/n2∑x2i−∑xi2/n
and
SSE=SST−SSR.
SST=
(Round to two decimal places as needed.)SSR=
(Round to two decimal places as needed.)SSE=
(Round to two decimal places as needed.)b. Compute the coefficient of determination,
r2=
(Round to four decimal places as needed.)
c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer.
_____________%
(Round to two decimal places as needed.)
d. State how useful the regression equation appears to be for making predictions. Choose the correct answer below.
Low usefulness
OR
Moderate to high usefulness
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