Question

A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below. Age (in years) Height (inches) 7 47.3 8 48.8 5 41.3 8 50.4 8 51 7 47.1 7 46.9 7 48 9 51.2 8 51.2 5 40.3 8 48.9 6 45.2 5 41.9 8 49.6 How much of the variation in the sample values of height does the model estimate

Answer 1

Answer:

0.940

Step-by-step explanation:

Given the data:

Age in years(X) _____Height(Y)

7 _________ 47.3

8 _________48.8

5 __________41.3

8 _________ 50.4

8 ___________51

7 __________47.1

7 __________46.9

7 ___________48

9 __________51.2

8 __________51.2

5 __________40.3

8 __________48.9

6 __________45.2

5 __________41.9

8 __________49.6

The proportion of Variation explained by the line of best fit in a regression model can be determined by calculating the Coefficient of determination (R²) of the model.

Using the online R² calculator, the variation in the sample values of height which is estimated by the model is 0.9696² = 0.94012416.

Hence about 0.94 or 94% variation in sample values of height is estimated by the model while (1 - 0.94 = 0.06 or 6%) is explained by other factors.