The following graph shows the relationship between head circumference and height in a sample of female healthcare students.
1. What kind of diagram is this?
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2. How would you describe the strength of this relationship?
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3. One of the statistics often calculated for data like these is a correlation coefficient, also known as Pearsonís correlation coefficient or the product moment correlation coefficient, usually denoted by r. What does this tell us?
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4. What do you think the value of the value of r might be for the relationship between head circumference and height?
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5. The significance test of the null hypothesis r = 0 in this population gave P < 0.0001. What does this mean and what precisely is it testing? How would you interpret the results of this test?
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6. What conditions or assumptions do the data have to meet for this test to be valid? Do you think they are met here?
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7. The program which was used to calculate r printed an approximate 95% confidence interval: 0.24 to 0.54. What does this tell us?
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8. What conditions or assumptions do the data have to satisfy for this confidence interval to be valid? Do you think these data meet them?
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9. The following graph shows the regression line for head circumference on height:
The equation of the regression line is:
head circumference = 372 + 0.114 ◊ height
What is a regression line and what does it tell us? In what units are 0.114 and 372 reported?
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10. The P value is P < 0.0001. What is this testing? What can we conclude from it?
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11. What assumptions are required for this test? Do you think they are met here? What further information would you like to assess this?
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12. Would we get a different P value if we carried out the regression of height on head circumference?
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13. How do the significance tests for the correlation coefficient being zero and the regression slope being zero compare? Are their assumptions different?
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14. The 95% confidence interval for the slope of the line is 0.067 to 0.161 mm per mm. What does this mean and what can we conclude from it?
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15. What assumptions do we require for the confidence interval to be valid? Are these different from those required for the confidence interval for the correlation coefficient?
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