Statistics 528 – Homework 4 Solutions
2.40
(a)
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Nitrates
Absorbance
Minitab gives the correlation 1.0 (in fact, .99994). Note that it is rounded up.
So, recalibration would not be necessary.
(b) The equation of the least squares line is Absorbance = 1.66 + 0.113 Nitrates.
At 500mg of nitrates per liter, the predicted absorbance is 58.16(=1.66 + 0.113*500). Because
the correlation is very close to 1, we expect that the prediction would be very accurate.
2.46
(a) Plot below.
(b) Correlation is 0.503. Rsquare is 0.253. The correlation 0.503 suggests that there is a
positive linear association between U.S. returns and overseas returns. However, the strength of
the linear relation is not high enough to predict overseas returns accurately based on U.S.
returns. The Rsquare 0.253 indicates that only 25.3% of variation in overseas returns can be
explained by linear regression on U.S. returns.
(c) Oversea = 4.76 + 0.663 US. For 1993, the predicted value is 11.46(=4.76+0.663*10.1), and
the actual value is 32.9.
(d) Predictions will not be very accurate because the correlation is low.
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 Winter '09
 Calder
 Regression Analysis, regression line, regression plot

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