P&K 3950

Sample: project B (quadratic regression)

Input data

CurrentConcentration
[mA][mg/m3]
5.048
7.3100
8.6146
4.417
5.760
6.898
7.1102
12.6209
11.7205
11.9201
14.3232
14.9242
10.7188
17.8280
16.1272
14.3238
16.7267
18.3296
18.1292
17.1274

Characteristics

Function: y'=A*x²+B*x+C

Coefficients
a
b
c
-0.7333
35.42
-114.9
Scatters 6.834
Determination coefficient  0.9947
Average value
xm
ym
11.97
188.3
Calculated values
Sxx
Syy
Sxy
427.7
1.501E+05
7914

List of function values

xy'Confidence intervalTolerance interval n'
  y1y2y3y4 
4.400026.76018.30435.2165.207948.3122.9091
5.663662.19556.18068.21041.91482.4765.7497
6.927295.28790.515100.0675.544115.039.1346
8.1908126.04121.40130.68106.35145.739.6750
9.4544154.45149.45159.44134.62174.288.3420
10.718180.52175.22185.81160.56200.477.4260
11.982204.24198.95209.53184.28224.207.4239
13.245225.62220.66230.59205.81245.448.4524
14.509244.67240.22249.12225.05264.2910.509
15.772261.37257.13265.60241.82280.9111.594
17.036275.72270.65280.80255.86295.598.0690
18.300287.74280.50294.98266.85308.633.9699

Confidence interval:

Valid for 95.0 percentage statistical certainty with table value t(17)= 2.1106

Tolerance interval:

Valid for 95.0 percentage statistical certainty with table value v(17)= 1.4004 and a share (1-gamma)=95.0 % of the entire collective

Function comparison (significance test)

Coefficients and scatter of the function:

StatementFunctionsABC
1y'=B*x+C 14.33 18.50 -33.12
2y'=A*x²+B*x+C 6.834 -0.7333 35.42 -114.9
3y'=B*ln(x)+C 6.093 192.0 -270.7
4y'=A*ln²(x)+B*ln(x)+C 5.678 14.87 124.8 -198.2
5y'=B*exp(x)+C 73.10 2.011E-06 160.6
6y'=A*exp²(x)+B*exp(x)+C 68.04 -5.733E-14 6.405E-06 149.1

The quadratic regression formula can be assumed as better than the linear one.

Test value:62.128
Table value F(17):4.4546
Statistical certainty:95%

Only statement 1 and 2 are compared.

Characteristics / limits

NameFactorTypeY-valueY(Type)delta YX
G 1--125  8.1474
G+V 1+V125129.674.66978.3466
1.2G+V1.2+V150154.984.98819.4794
2G+T 2+T250269.6519.65616.476
5%G 0.05--6.25  3.7037
10%G 0.1--12.5  3.9132


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