Homework Solution (#6)
Additional: Analysis of Urban Mortality data
Chapter 12. Nonlinear and Multiple Regression
1.
a).
ρ
(Mortality, Shs) = - 46358
228389 = - .4505
ρ
(Shs, Resid. Mort//SH) = 0
b). To create best possible multiple regression prediction equation with Shs and
one more predictor variable, we will choose %WhiteCollar since it has the biggest
absolute correlation with Residual.
2.
ρ
(Shs, %WhiteCollar) = .1659
-- It is making sense since as the sound housing in an area goes up, so should the
price of the house and the proportion of the white-collar;
ρ
(Shs, p<3) = -.4386
-- It is making sense since as sound housing goes up, the proportion of less
income people will go down;
ρ
(Shs, pop/house) = -.4228
-- It is making sense since as sound housing goes up, the income of family will go
up and less people have to live in each room.
3.
a). Rsquare = 55118/228398 = .241
b). Root Mean Square Error = 3040 = 55.14
c). Mean of Response = 940.3 (from JMP summary on page 8)
d). Shs -- t Ratio = -4.445/1.576 = - 2.82
e). Shs – Prob>|t| = P(| 57
t|> 2.82) = .006
f). pop/house -- Std Error = 74.12/1.697 = 43.68
g). pop/house – t Ratio = 2.88 = 1.697
h). pop/house – Prob>|t| = P(| 57
t|> 1.697) = .0951
i). Shs – F Ratio = 24194/3040 = 7.96
j). Shs – Prob > F = P( 1,57
F>7.96) = .006
k). pop/house – Sum of Squares = 55118 – 46358 = 8760
l). pop/house – F Ratio = 8760/3040 = 2.88
m). pop/house – Prob>F = P( 1,57
F>2.88) = .0951
n). Model – DF = 2
o). Model – Sum of Squares = 228398 – 173280 = 55118
p). Model – Mean Square = 55118/2 = 27559
