# Important information about correlation and regression

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Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Five fossil specimens have preserved both the femur and humerus bones. The measurements (in centimeters) for each bone are given below.

Femur 38 56 59 64 74

Humerus 41 63 70 72 84

Scientists are interested in determining if there is a strong relationship between two lengths of the two bones so that they might be persuaded that the five specimens belong to the same species. The Minitab output for regression is provided below.

MINITAB--Regression

The regression equation is humerus = -3.66 +1.20*femur

Predictor Coef StDev T P

Constant -3.660 4.459 -0.82 0.472

femur 1.19690 0.07509 15.94 0.0001

S=1.982 R-Sq = 98.8% R-Sq(adj) = 98.4%

Analysis of Variance

Source DF SS MS F P

Regression 1 998.21 998.21 254.10 0.001

Residual Error 3 11.79 3.93

Total 4 1010.00

a) Make a scatterplot of the data with femur length as the predictor variable

b) What is the scope of the regression equation?

c) What is the correlation coefficient, r?

d) Predict the length of a humerus for a fossil specimen with a femur that is 45 cm long.

e) Does the data suggest that the length of a femur and the length of a humerus are positively correlated? Test at the 0.01 level of significance. Be sure to explain your reasoning.

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##### Solution Summary

The solution makes a scatterplot of the data with femur length as the predictor variable, calculates the correlation coefficient and predict the length of a humerus for a fossil specimen with a femur that is 45 cm long.

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a) Make a scatterplot of the data with femur length as the predictor variable

b) What is the scope of the regression equation?

The equation would predict the values of the humerus from the values of femur in the range of values of femur that has been used to construct the regression equation.

c) What is the correlation coefficient, r?

R-Sq(adj) = 98.4%

correlation coefficient, r=square root of ...

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