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1. Sir Francis Galton, a cousin of James Darwin, examined the relationship betwe

ID: 2923402 • Letter: 1

Question

1. 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:

          StudentH=19.6+0.73×Midparh,R^2=0.45,SER=2.0

where StudentH is the height of students in inches, and Midparh is the average of the parental heights. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.)

(a) What is the prediction for the height of a child whose parents have an average height of 67 inches?

(b) How would the regression estimates change if height is measured in centimeters? Give all results, slope coefficient, intercept coefficient,R^2, SER.

Explanation / Answer

a)

The given linear regression equation is,

StudentH=19.6+0.73×Midparh

given that  parents have an average height of 67 inches

StudentH = 19.6 + 0.73 × 67

= 19.6 + 48.91

= 68.51

StudentH = 68.51

prediction for the height of a child whose parents have an average height of 67 inches is 68.51 inches.

b)

The given regression model linear in terms of parameters therefore regression estimates does not change if height is measured in centimeters.

all the results remains same.

intercept coefficient = 19.6

slope coefficient = 0.73

R2 = 0.45

SER = 2.0