Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (The pair of variables have a significant​ correlation.) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The table below shows the heights​ (in feet) and the number of stories of six notable buildings in a city. Height comma x 764 625 520 510 492 484 ​(a) xequals498 feet ​(b) xequals641 feet ​Stories, y 55 47 44 41 38 35 ​(c) xequals345 feet ​(d) xequals728 feet

Answer 1

Sum of X = 3395
Sum of Y = 260
Mean X = 565.8333
Mean Y = 43.3333
Sum of squares (SS_X) = 60136.8333
Sum of products (SP) = 3704.3333

Regression Equation = ŷ = bX + a

b = SP/SS_X = 3704.33/60136.83 = 0.0616

a = M_Y - bM_X = 43.33 - (0.06*565.83) = 8.4789

ŷ = 0.0616X + 8.4789

a. For x=498,

ŷ = (0.0616*498)+ 8.4789=39.1557

b. x=641,

ŷ = (0.0616*641)+ 8.4789=47.9645

c. x=345,

ŷ = (0.0616*345)+ 8.4789=29.7309

d. x=728,

ŷ = (0.0616*728)+ 8.4789=53.3237