Key
A.P. Statistics
HW 4 – p. 192 (43, 45, 55, 60,62)
(43)
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Key
The dotted line is the line yˆ  x  1 and the solid line is the line
yˆ  3  2 x. The dotted line comes closer to all of the data points.
Thus, the line yˆ  x  1 fits the data best.
yˆ  5.43  0.005350  5.165
Actual Value: y  5.08
Residual = y  yˆ  5.08  5.165  0.085
(45)
Predicted Value:
(55)
The least squares regression equation is yˆ  31.934  0.304 x.
x
%
Return
74
66
81
52
73
62
52
45
62
46
60
46
38
y
New
Adults
5
6
8
11
12
15
16
17
18
18
19
20
20
ŷ
y  yˆ
9.4366
11.869
7.3084
16.125
9.7406
13.085
16.125
18.253
13.085
17.949
13.693
17.949
20.381
Residual
-4.437
-5.869
0.6916
-5.125
2.2594
1.9152
-0.1251
-1.253
4.9152
0.0508
5.3071
2.0508
-0.3814
The predicted pH level was bigger than the
real pH by 0.085.
r
 0.98
 0.748
12
a  y  bx
a  14.23  (0.304)(58.23)
(a)
NewAdults
% Return
(60)
(62)
The residual plot clearly shows that the prediction errors
increase for larger laboratory measurements. In other words,
the variability in the field measurements increases as the
laboratory measurements increase. The least squares line
does not provide a great fit, especially for larger depths.
We would certainly not use the regression
line to predict fuel consumption. The
scatterplot shows a nonlinear relationship.
br
 5.29 
 0.748

sx
 13.03 
sy
Good residual plot;
No obvious pattern.