Sir Francis Galton, in the late 1800s, was the first to introduce the statistica
ID: 3178585 • Letter: S
Question
Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. The value of the sample correlation coefficient for these data is approximately 0.797. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 93.754194 + 0.48681423 x
Sample size: 15
R (correlation coefficient) = 0.79686554
R-sq = 0.63499469
Estimate of error standard deviation: 5.0598157
Parameter estimates:
Hence,
Slope = 0.49
Intercept = 93.75
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 93.754194 18.348943 0 13 5.1095146 0.0002 Slope 0.48681423 0.10236609 0 13 4.7556198 0.0004