419
Chapter 18
18.1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.4924
R Square 0.2425
Adjusted R Square 0.2019
Standard Error 40.24
Observations 60
ANOVA
df SS MS F Significance F
Regression 3 29030 9677 5.97 0.0013
Residual 56 90694 1620
Total 59 119724
Coefficients Standard Error t Stat Pvalue
Intercept 51.39 23.517 2.19 0.0331
Lot size 0.700 0.559 1.25 0.2156
Trees 0.679 0.229 2.96 0.0045
Distance 0.378 0.195 1.94 0.0577
a 3 2 1 378 . 679 . 700 . 39 . 51 & x x x y  + + =
b The standard error of estimate is e s = 40.24. It is an estimate of the standard
deviation of the error
variable.
c The coefficient of determination is 2 R = .2425; 24.25% of the variation in
prices is explained by the
model.
d The coefficient of determination adjusted for degrees of freedom is .2019. It
differs from
2 R because it includes an adjustment for the number of independent variables.
e : 0 H = ß1 = ß2 = ß3 0
: 1 H At least one i ß is not equal to zero
F = 5.97, pvalue = .0013. There is enough evidence to conclude that the model is
valid.
f 1 b = .700; for each addition thousand square feet the price on average increases
by .700 thousand
dollars provided that the other variables remain constant.
2 b = .679; for each addition tree the price on average increases by .679 thousand
dollars provided that
the other variables remain constant.
3 b = .378; for each addition foot from the lake the price on average decreases by
.378 thousand
dollars provided that the other variables remain constant.
420
g : 0 H = ßi 0
: 1 H i ß . 0
Lot size: t = 1.25, pvalue = .2156
Trees: t = 2.96, pvalue = .0045
Distance: t = 1.94, pvalue = .0577
Only for the number of trees is there enough evidence to infer a linear
relationship with price.
18.2
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8734
R Square 0.7629
Adjusted R Square 0.7453
Standard Error 3.75
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View Full DocumentObservations 30
ANOVA
df SS MS F Significance F
Regression 2 1223.18 611.59 43.43 0.0000
Residual 27 380.18 14.08
Total 29 1603.37
Coefficients Standard Error t Stat Pvalue
Intercept 13.01 3.528 3.69 0.0010
Assignment 0.194 0.200 0.97 0.3417
Midterm 1.112 0.122 9.12 0.0000
a 2 1 112 . 1 194 . 01 . 13 & x x y + + =
b The standard error of estimate is e s = 3.75. It is an estimate of the standard
deviation of the error
variable.
c The coefficient of determination is 2 R = .7629; 76.29% of the variation in final
exam marks is
explained by the model.
d The coefficient of determination adjusted for degrees of freedom is .7453. It
differs from
2 R because it includes an adjustment for the number of independent variables.
e : 0 H = ß1 = ß2 0
: 1 H At least one i ß is not equal to zero
F = 43.43, pvalue = 0. There is enough evidence to conclude that the model is
valid.
f 1 b = .194; for each addition mark on assignments the final exam mark on average
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 Spring '08
 ROCHON
 Statistics, Normal Distribution, Regression Analysis, Standard Error, Variance, Prediction interval

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