Answer

Correlation Coefficient

The correlation coefficient measures the degree of a relationship between two variables. The point of focus in this study is the relationship between age and height. When children are born, they grow and increase in height even though the rate of increase depends on a child. This fact depicts that age and height have a positive relationship in children. Nonetheless, as people age, the pattern of growth in their heights tends to change, and to some extent, decrease. This variance brings the interest to study whether the relationship between the two variables is statistically significant. Thus, what follows in this paper is a sample correlation coefficient of age and height from data of 40 adults.

Correlation Coefficient between Age and Height

Excel Output

According to the excel output, the correlation coefficient for the sample data is -0.09824. The significance test from 95% Critical Values of the Sample Correlation Coefficient Table at 38 (40 – 2) degrees of freedom with a p-value of p < 0.05 gives a critical value of 0.325. Since the correlation coefficient falls between the negative critical value and the positive critical value, it implies that r is not significant. Therefore, the relationship between age and height for this sample data cannot be predicted using a line.

The absolute value of the coefficient is between 0 and 0.2, interpreted as a very weak correlation. However, the negative correlation coefficient signifies that an increase in age has a slight negative impact on height. This change cannot be predicted using a linear model because the strength of the association is very weak and does not always happen with the same percentage. Hence, this analysis shows that adult heights are partly associated with their ages.