12.We have developed a regression equation to predict son’s height from father’s height: Y = 19.4 + .737x a. What is the intercept? b. What is the slope? c. What is the predicted son’s height when the father’s height is 70.8 inches?

(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

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

3

step-by-step explanation: