The Term Regression Was Originally Used In 1885 By Sir Francis Galto 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.” In 1903, two statisticians, K. Pearson and A. Lee, examined Galton's law using a sample of 1,078 father—son pairs. They modeled the relationship with a regression line; the line was Son's height = 33.73 + 0.516 × Father’s height. Interpretation of the coefficients: The intercept, 33.73, represents the estimated son’s height when the father’s height is zero, which is not meaningful in real-world terms but is statistically necessary for the model. The slope coefficient, 0.516, indicates that for each additional inch (or unit) of father’s height, the son’s height increases by approximately 0.516 inches, illustrating the partial inheritance of height traits and juvenile regression toward the mean. The regression line suggests that sons of tall fathers tend to be taller, but the slope less than 1 indicates the son's height does not increase proportionally with the father's height. Instead, there is a tendency for the son's height to regress toward the average, especially when fathers are exceptionally tall or short. For sons of tall fathers, the line forecasts that their height will be higher, but not proportionally so, and the same applies for sons of shorter fathers. Overall, the line indicates that while there is a positive relationship between father and son heights, the strength of this relationship is moderate, due to a slope less than 1. Regression Analysis of Florida Condominium Prices and Floor Levels A real estate agent analyzing 1,200 sq. ft. condominiums in Florida observed that prices varied among units within the same building. Recognizing that floor level might influence sale prices, the agent recorded sale prices (in $1,000s) and floor numbers for these units. Using this data, the regression model was constructed to analyze the relationship between the floor level and the condo's sale price. a. To determine the regression line, statistical software or manual calculations involving means, variances, and covariances are utilized. The typical form of the line is Price = a + b × Floor, where b is the slope coefficient indicating how much the price increases per additional floor, and a is the intercept representing the estimated price at floor zero (below ground or at ground level). Once computed, the model might take the form: Price = 50 + 10 × Floor (as an example), suggesting each additional floor adds approximately $10,000 to the condo’s sale price.
The Term Regression Was Originally Used In 1885 By Sir Franc
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