Testing the Coefficient of Correlation.

4. Testing the coefficient of correlation Is there a linear relationship between a male's adult height and his father's adult height? Is there is a linear relationship between a male's adult height and the adult height of his male cousin? Suppose that a genealogist investigates these questions. She hypothesizes that there is a linear relationship between a son's height and his father's height. She hypothesizes that there is not a linear relationship between a son's height and the height of his male cousin. The population of interest is families with at least one son and at least one male cousin of the son (or sons). A random sample of 30 families is selected from the target population. The sample data are stored in the FatherSon data set in the DataView tool. Sample Variables : 3 Observations : 30 Heights of San, Father, and Son&"\"s Cousin > Observations Variable V Type V Form V Values V Missing V I I Son's Height Quantitative Numeric 30 D - Fathers Height Quantitative Numeric 30 D Cuusin's Height Quantitative Numeric 30 0 Variable Variable Variable Correlation Correlation Analyze the relationship between a son's height and his father's height by calling up a scatter diagram in the tool. The scatter diagram suggests that there V a linear relationship between a son's height and his father's height. Analyze the relationship between a son's height and his cousin's height by calling up a scatter diagram in the tool. The scatter diagram suggests that there V a linear relationship between a son's height and his cousin's height. The genealogist is only interested in whether a son's height is linearly related to the height of a male relative. She is not interested in the form of the linear relationship. Therefore, it 7 necessary to estimate the linear regression model provided that (son's height, father's height) and (son's height, cousin's height) follow a V distribution. The sample covariance sxy between a son's height and his father's height is 0.08923. Test the hypothesis that there is no linear relationship between a son's height and his father's height. The test statistic is t = V , and you V infer that there is a linear relationship between the heighis. The sample covariance sly between a son's height and his cousin's height is 0.001394. Test the hypothesis that there is no linear relationship between a son's height and his cousin's height. The test statistic is t = V , and you 7 infer that there is a linear relationship between the heights