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


Requried:

a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?

b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?

c. How much of the variation in the sample values of height does the model estimated in part (b) explain?

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Age(x)

7

8

5

8

8

7

7

7

9

8

5

8

6

5

8

Height (Y)

47.3

48.8

41.3

50.4

51

47.1

46.9

48

51.2

51.2

40.3

48.9

45.2

41.9

49.6

The estimated regression equation:

ŷ = 2.73953X + 27.91395

Where ;

X = independent variable

ŷ = predicted or dependent variable

27.91395 = intercept

C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:

Using the online pearson correlation Coefficient calculator :

The correlation Coefficient is 0.9696.

which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.