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.

Height of father, Height of son, y (in centimeters) in centimeters) 155.8 188.2 186.2 202.4 174.4 174.7 187.6 192.4 175.9 175.3 191.3 181.9 210 200 190 184.4 202.2 170.0 161.0 175.3 190.5 180.8 189.4 192.0 170.7 158.9 195.8 186.8 190.2 189.8 150 160 170 80 90 200 210 Figure1 166.8 The value of the sample correlation coefficientr for these data is approximately 0.798 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

Answer 1

The least square regression equation for the sample is calculated as

$wNqlamG8q1C2wAAAABJRU5ErkJggg==$

Now

$zHfxf+9780wVdNRSKd3AAAAABJRU5ErkJggg==$

Regression Equation = ŷ = bX + a

Where,

b= Slope and a= y-intercept now,

Sum of X = 2885.1
Sum of Y = 2903.6
Mean X = 180.3188
Mean Y = 181.475
Sum of squares (SS_X) = $\sum (X - Mx)2=3068.9844$
Sum of products (SP) = $\sum (X - Mx)(Y - My)=1549.7375$

b = SP/SS_X = 1549.74/3068.98 = 0.51

a = M_Y - bM_X = 181.48 - (0.5*180.32) = 90.42