Question

Problems 4-6 Measurements of 49 sparrows were used to create a model using the length of the humerus bone to predict the total length of the bird. The model was calculated as: Total length-80.8+4.2 Humerus Both lengths are measured in centimeters. Use the model to predict the total length of a sparrow with a humerus that measures 19 centimeters. a 104 cm 4. d. 1615 cm b. 160.6 cm C. 2866 cm 5. In the model from the above problem, what does the number 4.2 mean? If the bird has a humerus length of zero, the total length will be 4.2 cm. This number does not make a sense in this context but might in other contexts. b. If the bird has a humerus length of 4.2, the total length will be 80.8 cm. c. If the humerus length increases by 1 cm, the total length increases by 4.2 cm. d. If the total length increases by 1 cm, the humerus length increases byt 4.2 cm. When the sparrow model was fitted, the coefficient of determination was reported as R-sq 0.416. What 6. does this mean? The length of the humerus is 41.6% of the total length of the bird. 41.6% of the data is within one standard deviation of the mean. 41.6% of the variation in the total length is explained by this model. a. b, dy 41.5% of the length of the humerus is explained by this model.

Answer 1

Solution(4)
Give regression equation
Total length = 80.8 + 4.2*Humerus
Given X = 19
So Total length = 80.8 +4.2*19 = 80.8 + 79.8 = 160.6cm
So its answer is B. i.e. 160.6cm
Solution(5)
Its answer is C. i.e. If the humerus length increases by 1 cm, the total length will increase by 4.2 cm.
Solution(6)
If R^2 = 0.416
Its answer is C. i.e. 41.6% of the variation in the total length is explained by this model.