Correlation

Posted: August 26th, 2021

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Question 4

1. Correlation

The father’s education has a positive correlation with childhood height as an increase in the education level leads to a corresponding increase in the child’s height. When the education level is at 0.13, the child’s height is 0.06, and an increase in education to 0.20 leads to a corresponding increase to 0.12. However, the mother’s education does not correlate with the child’s height. As indicated, when the mother’s education level is at 0.34, the child’s height is at 0.06, and an increase in the education level to 0.41 corresponds to a decrease of 0.05 in the child’s height. Further increase in the mother’s education level to 0.58 leads to an increaseto 0.13 in the child’s height.

• Null hypothesis

Null Hypothesis

There is no correlation between a child’s height and his mother’s education in the sampled population.

Alternative Hypothesis

There is a correlation between a child’s height and his mother’s education in thechanges of co-efficient. When the probability of observation in the test statistic is less than the 10% significance level (90% Confidence Interval), then reject the null hypothesis in the sample test.

• Change in coefficient

Columns 1 and 2 will not change as there is no father’s data on the years of education in the two columns. In the case of a null hypothesis, a father’s education does not affect the child’s education. Hence, columns 3 and 4 will not have any changes as there is no direct correlation between the mother’s education and the child’s height.

• F-Test

When column 3, which contain the mother’s year of education is the unrestricted model, the restricted model on the father’s education is as below;

• Test Statistics