If One Animal Tends to Live Longer Than Another, Would You Expect It to Have a Longer Gestation

If one animal tends to live longer than another, would you expect it to have a longer gestation period than the other?

1. Use your calculator to determine the least squares regression line for predicting an animal’s gestation period from its longevity and store the equation in Y1:
2. Interpret the slope of the regression line in the context of the problem.

1. What proportion of the variability in the animals’ gestation period is explained by the regression line?
2. Which animal has the largest residual? Is its gestation period longer or shorter than expected for an animal with its longevity?

1. Remove that animal from the list. Recalculate the regression line. Is there a substantial difference? Is that animal an influential observation?
2. Return that animal to the list. Now remove the data for the elephant. Recalculate the LSRL:

1. In which case did the removal of one animal affect the regression line more?

During the first 3 centuries AD, the Roman Empire produced coins in the Eastern provinces. Some historians argue that not all these coins were produced in local mints, and further that the mint of Rome struck some of them. Because the "style" of coins is difficult to analyze, the historians would like to use metallurgical analysis as one tool to identify the source mints of these coins. Investigators studied 11 coins known to have been produced by local mints in an attempt to identify a trace element profile for these coins, and have identified gold and lead as possible factors in identifying other coins as having been locally minted. The gold and lead content, measured as a % of weight of each coin, is given in the table at right, and a scatter plot of these data is presented below.

1. a) What is the equation of the least squares

regression line?

b) What is the value of the correlation

coefficient? Interpret this value.

c) What is the value of the coefficient of determination? Give an interpretation of this value.

2. Suppose that the locally minted coins analyzed in problem 1 are representative of the metallurgical content of mints in the Eastern provinces of the Roman Empire during the first 300 years AD.

a) If a locally minted coin is selected at random, and its gold content is 0.30% by weight, calculate the predicted lead content. Be sure to use correct notation and units.

b) One of the coins used to calculate the regression equations has a gold content of 0.300%. Calculate the residual for this coin. Be sure to use correct notation and units.

3. When children and adolescents are discharged from the hospital the parents may still provide substantial care, such as the insertion of a feeding tube through the nose and down the esophagus into the stomach. It is difficult for parents to know how far to insert the tube, especially with rapidly growing infants. It may be possible for parents to measure their child’s height and from that calculate the appropriate insertion length using a regression equation. At a major children’s hospital, children and adolescents’ heights and esophageal lengths were measured and a regression analysis performed. The data from this analysis is summarized below:

Summary statistics from Regression Analysis

Height (cm) and Esophageal Length (cm)

a) For a child with a height one standard deviation above the mean, what would be the

predicted esophageal length?

b) What proportion of the variability in esophageal length is accounted for by the height

of the children and adolescents?

c) From the information presented above, does it appear that the esophagus length can be accurately predicted from the height of young patients? Provide statistical evidence for your response.