Question 145719: 1. Nancy Giggles has not been doing well on statistics examinations. She decides to sample 12 of her friends to determine the number of hours spent studying for Test 3 and the score out of 100 received on that test. The results:
Test 4 Score Hours of study
47 7
55 10
87 39
98 43
37 2
71 12
100 51
98 48
85 23
82 26
56 7
78 14
(i) Find the equation of the regression line using the least square technique. Interpret the meanings conveyed by the regression equation.
(ii) Compute the correlation coefficient and the coefficient of Determination. Interpret these values.
2. David Gallano, a wine merchant, has selected opinions on grape wine quality from a random sample of his customers. The customers tasted wine made from grapes grown in three regions of the country. The customers rated wine quality on a scale of 1 (best) to 4 (worst). The sample data looks like:
Customer Quality Rating of Wine by Grape-growing region
Quality Rating
Growing Region
I Growing Region
II Growing Region
III Row Total
1 15 10 6 31
2 7 13 12 32
3 11 12 8 31
4 3 8 15 26
Column Total
36 43 41 120
David wants to know whether quality ratings are independent of the grape-growing region. Can you conclude at a 95% confidence that the quality rating is independent of the growing region?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Comment: I changed a couple of words in the "meaning of r^2"
explanation.
Cheers,
Stan H.
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Nancy Giggles has not been doing well on statistics examinations. She decides to sample 12 of her friends to determine the number of hours spent studying for Test 3 and the score out of 100 received on that test. The results:
Test 4 Score Hours of study
47 7
55 10
87 39
98 43
37 2
71 12
100 51
98 48
85 23
82 26
56 7
78 14
(i) Find the equation of the regression line using the least square technique. Interpret the meanings conveyed by the regression equation.
test score = 1.1128(hrs of study) + 48.35..
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(ii) Compute the correlation coefficient and the coefficient of Determination. Interpret these values.
-----------------------------
r = 0.918168...
r is a measure of the strength of the linear relationship between the variables.
-----------------------------
r^2 = 0.8430...
84.3% of the variability in the test scores is explained by the regression equation.
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2. David Gallano, a wine merchant, has selected opinions on grape wine quality from a random sample of his customers. The customers tasted wine made from grapes grown in three regions of the country. The customers rated wine quality on a scale of 1 (best) to 4 (worst). The sample data looks like:
Customer Quality Rating of Wine by Grape-growing region
Quality Rating
Growing Region
I Growing Region II Growing Region III Row Total
1 15 10 6 31
2 7 13 12 32
3 11 12 8 31
4 3 8 15 26
Column Total
36 43 41 120
David wants to know whether quality ratings are independent of the grape-growing region. Can you conclude at a 95% confidence that the quality rating is independent of the growing region?
Ho: they are independent
Ha: they are dependent
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I ran a Chi-Sq on the 4 x 3 set of data and got the following results:
Chi-Sq = 14.9760...
p-value = 0.02044...
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Conclusion: Since p-value is less than 5%, reject Ho.
The quality rating and growing region are dependent variables.
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Cheers,
Stan H.
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