0。62869x1x3+10。35923x1x4+0。036191x2x3+

1。12906x2x4−0。65758x3x4−1。81058 x2 −9。48279×

Usually, the desired confidence level is set as  95%。 If the P-value of model is smaller than 0。05, the regression model is considered to be statistically significant,   and   the   variables   in   the   model     have

significant effects on the response。 When   R

Dt=33。22430+606。08433x1−543。64845x2−1307。48504x3−

83。08908x4 +906。29582x1 x2 −2668。62630x1 x3 −

70。35251x1x4−901。22357x2x3+75。44490x2x4+

69。95454x3x4+273。60843 x2 +293。84858 x2 +

to unity, the better the response model fits the actual data, the less the difference between the predicted and actual values exists。 If those additional terms don’t add value to the model, the adjusted  R-squared ( R 2 ) decreases  with

the number of terms in the model increasing。  Therefore,

3 4 the bigger the value of the adjusted R-squared is, the

where x1 represents the fillet radius;  x2  represents position of draw-bead; x3 represents the blank size; x4 represents blank-holding force。 The regression equations could show an approximate relationship between the response variables and the independent variables。 The fitted formulations can be applied to predicting  the values of Df, Dw and Dt。

4。2Analysis of proposed mathematical model

To evaluate the reliability of the  experimental results and the credibility of the response models, both the statistical significance of the regression models and the statistical significant of the inpidual model coefficients need to be tested。 These tests are performed with ANOVA procedure by calculating the ‘‘F-value’’, the  “P-value’’,  the  determination  coefficients  (R2),  as

well as the adjusted R-squared ( R 2 )。

better the regression effects are。

Table 3 presents the analysis of variance (ANOVA) results of the Df model。 The significance of each coefficient is determined by using T-test  and P-value。 The table shows that the P-value of model is less than significance level α (α=0。05), indicating that the terms in

the model have a significant effect on the Df。 The total determination coefficient (R2) is 0。8691, suggesting that the  polynomial  model  can  represent  the  experimental

results adequately。 The adjusted  determination coefficient ( R 2 ) is 0。7469, which implies that 74。69% of the changes of this model are attributed to the independent  variables。  The  ANOVA  results  show that

the model F-value is 7。11 (F＞F0。05  (14, 30=2。31),    and

the model P-values is 0。0003, which is far less than 0。05。 Both the F-value and the P-value demonstrate that the regression result is very significant。

Table 3 Analysis of variance (ANOVA) for Df

Source Sum of squares Df Mean square F-value P-value Prob>F

Model 423。51 14 30。25066 7。111295 0。0003 Significant

x1