Question 145859
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.
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r = 0.918168...
r is a measure of the strength of the linear relationship between the variables.
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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.