P&K 3950

Sample: project B (quadratic regression)

Input data

Current Concentration
[mA] [mg/m3]
5.0 48
7.3 100
8.6 146
4.4 17
5.7 60
6.8 98
7.1 102
12.6 209
11.7 205
11.9 201
14.3 232
14.9 242
10.7 188
17.8 280
16.1 272
14.3 238
16.7 267
18.3 296
18.1 292
17.1 274

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

Name Factor Type Y-value Y(Type) delta Y X
G 1 -- 125     8.1474
G+V 1 +V 125 129.67 4.6697 8.3466
1.2G+V 1.2 +V 150 154.98 4.9881 9.4794
2G+T 2 +T 250 269.65 19.656 16.476
5%G 0.05 -- 6.25     3.7037
10%G 0.1 -- 12.5     3.9132


Smarte Lösungem. Für alle Plattformen



  
Width :

Language:





      Accept Cookies