(Continuation from Chapter 4)Sir Francis Galton,a Cousin of James Darwin,examined

question 14

Essay

(Continuation from Chapter 4)Sir Francis Galton,a cousin of James Darwin,examined the relationship between the height of children and their parents towards the end of the 19th century.It is from this study that the name "regression" originated.You decide to update his findings by collecting data from 110 college students,and estimate the following relationship: = 19.6 + 0.73 × Midparh,R2 = 0.45,SER = 2.0
(7.2)(0.10)
where Studenth is the height of students in inches,and Midparh is the average of the parental heights.Values in parentheses are heteroskedasticity robust standard errors.(Following Galton's methodology,both variables were adjusted so that the average female height was equal to the average male height. )
(a)Test for the statistical significance of the slope coefficient.
(b)If children,on average,were expected to be of the same height as their parents,then this would imply two hypotheses,one for the slope and one for the intercept.
(i)What should the null hypothesis be for the intercept? Calculate the relevant t-statistic and carry out the hypothesis test at the 1% level.
(ii)What should the null hypothesis be for the slope? Calculate the relevant t-statistic and carry out the hypothesis test at the 5% level.
(c)Can you reject the null hypothesis that the regression R2 is zero?
(d)Construct a 95% confidence interval for a one inch increase in the average of parental height.

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Definitions:

Health Promotion

The method of empowering individuals to enhance their ability to govern, and to better, their own well-being.

Stranger Danger

A concept taught to children to alert them to the potential risks posed by people they do not know.

Adolescents

Individuals in the transitional stage of development between childhood and adulthood, generally ranging from 13 to 19 years of age, characterized by rapid physical, emotional, and social changes.

Health Promotion

Efforts aimed at enhancing the quality of health and well-being of individuals and communities through prevention, awareness, and lifestyle changes.