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Correlation & Regression Analysis

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Statistics Problems
1. Given: The paired sample data of the age and alcohol consumption of men result in a linear correlation coefficient close to 0.

Conclusion: Older men tend to consume more alcohol than young men

What is the error in the stated conclusion?

2. The eruption height and the time interval after eruption of a geyser were measured and are:
Height (X) 115 95 100 125 135 105 95 85
Interval After (y) 67 80 30 58 62 76 69 40

What is the value of the linear coefficient r?
What is the critical value of r from the table showing the critical values for the Pearson Correlation coefficient using, coefficient=0.05?
Is there a linear correlation between the two variables?

3. Express the null hypothesis H(o) and the alternative hypothesis H (1) in symbolic form.
The mean weight of women who won a beauty pageant is equal to 121 lbs.

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The solution provides step by step method for the calculation of correlation and regression analysis. Formula for the calculation and Interpretations of the results are also included.

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Correlation and regression analysis.

QUESTIONS:
(a) How does correlation analysis differ from regression analysis?
(b) What does a correlation coefficient reveal?
(c) State the quick rule for a significant correlation and explain its limitations.
(d) What sums are needed to calculate a correlation coefficient?
(e) What are the two ways of testing a correlation coefficient for significance?

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