To study the relationship between soil pH (x) and A1 (y), usethe data found. a)
ID: 2914532 • Letter: T
Question
To study the relationship between soil pH (x) and A1 (y), usethe data found.
a) Find the best polynomial model forthis data.
c) Which of these models in parts a)and b) is better?
d) Find a 94% Confidence interval for eachof the bj’s in your models, and interpret.
e) Find a 93% PredictionInterval for y, when x = 4.25 using the model in part b). Does thepoint estimate for y when x = 4.25 using model a) fall in thisinterval?
X
Y
4.01
1.2
4.07
0.78
4.08
0.83
4.1
0.98
4.18
0.65
4.2
0.76
4.23
0.4
4.27
0.45
4.3
0.39
4.41
0.3
4.45
0.2
4.5
0.24
4.58
0.1
4.68
0.13
4.7
0.07
4.77
0.04
X
Y
4.01
1.2
4.07
0.78
4.08
0.83
4.1
0.98
4.18
0.65
4.2
0.76
4.23
0.4
4.27
0.45
4.3
0.39
4.41
0.3
4.45
0.2
4.5
0.24
4.58
0.1
4.68
0.13
4.7
0.07
4.77
0.04
Explanation / Answer
The regression equationis
y = 46.9 - 19.9 x + 2.12 x_sqr
Predictor Coef SECoef T P
Constant 46.907 9.432 4.97 0.000
x -19.909 4.310 -4.62 0.000
x_sqr 2.1161 0.4911 4.31 0.001
S = 0.0933212 R-Sq = 94.0% R-Sq(adj) =93.1%
Analysis of Variance
The regression equation is
y = 6.31 - 1.34 x
Predictor Coef SECoef T P
Constant 6.3057 0.6426 9.81 0.000
x -1.3429 0.1477 -9.09 0.000
S = 0.140129 R-Sq = 85.5% R-Sq(adj) =84.5%
Analysis of Variance
Source DF SS MS F P
Regression 1 1.6241 1.6241 82.71 0.000
Residual Error 14 0.2749 0.0196
Total 15 1.8990
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