The term regression was originally used in 1885 by Sir Francis Galton in his analysis of the relationship between the heights of children and parents. He formulated the “law of universal regression,” which specifies that “each peculiarity in a man is shared by his kinsmen, but on average in a less degree.” (Evidently, people spoke this way in 1885.) In 1903, two statisticians, K. Pearson and A. Lee, took a random sample of 1,078 father —son pairs to examine Galton's law (“On the Laws of Inheritance in Man, I. Inheritance of Physical Characteristics,” Biometrika 2:457–462). Their sample regression line was
Son's height = 33.73 + .516 × Father's height
a. Interpret the coefficients.
b. What does the regression line tell you about the heights of sons of tall fathers?
c. What does the regression line tell you about the heights of sons of short fathers?
Florida condominiums are popular winter retreats for many North Americans. In recent years, the prices have steadily increased. A real estate agent wanted to know why prices of similar-sized apartments in the same building vary. A possible answer lies in the floor. It may be that the higher the floor, the greater the sale price of the apartment. He recorded the price (in $1,000s) of 1,200 sq. ft. condominiums in several buildings in the same location that have sold recently and the floor number of the condominium.
a. Determine the regression line.
b. What do the coefficients tell you about the relationship between the two variables?
Refer to Exercise 16.6.
a. What is the standard error of estimate? Interpret its value.
b. Describe how well the memory test scores and length of television commercial are linearly related.
c. Are the memory test scores and length of commercial linearly related? Test using a 5% significance level.
d. Estimate the slope coefficient with 90% confidence.
Pick any 1 (or more) of the 11 exercises above and...