Answer:
(a) 19.4
(b) 0.737
(c) 71.6 inches
Step-by-step explanation:
This is a linear regression as it follows the general equation of a line given by;
y = mx + c ---------------(i)
Where;
y = value of a given point on the line along the y-axis
x = value of a given point on the line along the x-axis
m = gradient/slope of the line
c = y-intercept of the line.
Now, the given regression equation to predict son's height from father's height is;
y = 19.4 + 0.737x ------------(ii)
Equation (ii) can be re-written as;
y = 0.737x + 19.4 -----------------(iii)
Where;
x = father's height
y = predicted son's height
Now, comparing equations(i) and (iii) shows that;
m = slope = 0.737
c = intercept = 19.4
(i) The intercept of the regression equation is thus 19.4
(ii) The slope of the equation is 0.737
(iii) The predicted son's height when the father's height is 70.8 inches can be calculated by substituting x = 70.8 into equation (iii) as follows;
y = 0.737(70.8) + 19.4
y = 71.6inches
