用5个定理给出最小一乘线性回归的相关性质,为其工程应用奠定了基础。文中首先证明了“由“最小一乘”准则确定的直线y=b1x1+ b2x2经过其两个样本点”以及“由最小一乘准则确定的直线y=b1x1+ b2x2+a经过其三个样本点”。然后应用数学归...用5个定理给出最小一乘线性回归的相关性质,为其工程应用奠定了基础。文中首先证明了“由“最小一乘”准则确定的直线y=b1x1+ b2x2经过其两个样本点”以及“由最小一乘准则确定的直线y=b1x1+ b2x2+a经过其三个样本点”。然后应用数学归纳法得到如下定理:设有n(n>P)个样本点(x1i, x2i, ? xP i, yi,),则由最小一乘准则确定的线性非奇次模型y=b1x1+b2x2+?bPxP+a经过其P+1个样本点,而相应的奇次模型必经过其P个样本点。通过大量工程实例证实了最小一乘具有较强的稳健性,同时也证实了定理的正确性。展开更多
On the basis of Thirlwall’s framework (1966),this paper develops a model to analyze the correlation between regional disparities and industry structure.The empirical results show that the differences of industry stru...On the basis of Thirlwall’s framework (1966),this paper develops a model to analyze the correlation between regional disparities and industry structure.The empirical results show that the differences of industry structure cannot fully account for regional economic disparities.展开更多
A systematic approach was presented to develop the empirical model for predicting the ultimate tensile strength of AA5083-H111 aluminum alloy which is widely used in ship building industry by incorporating friction st...A systematic approach was presented to develop the empirical model for predicting the ultimate tensile strength of AA5083-H111 aluminum alloy which is widely used in ship building industry by incorporating friction stir welding(FSW) process parameters such as tool rotational speed,welding speed,and axial force.FSW was carried out considering three-factor five-level central composite rotatable design with full replications technique.Response surface methodology(RSM) was applied to developing linear regression model for establishing the relationship between the FSW process parameters and ultimate tensile strength.Analysis of variance(ANOVA) technique was used to check the adequacy of the developed model.The FSW process parameters were also optimized using response surface methodology(RSM) to maximize the ultimate tensile strength.The joint welded at a tool rotational speed of 1 000 r/min,a welding speed of 69 mm/min and an axial force of 1.33 t exhibits higher tensile strength compared with other joints.展开更多
文摘用5个定理给出最小一乘线性回归的相关性质,为其工程应用奠定了基础。文中首先证明了“由“最小一乘”准则确定的直线y=b1x1+ b2x2经过其两个样本点”以及“由最小一乘准则确定的直线y=b1x1+ b2x2+a经过其三个样本点”。然后应用数学归纳法得到如下定理:设有n(n>P)个样本点(x1i, x2i, ? xP i, yi,),则由最小一乘准则确定的线性非奇次模型y=b1x1+b2x2+?bPxP+a经过其P+1个样本点,而相应的奇次模型必经过其P个样本点。通过大量工程实例证实了最小一乘具有较强的稳健性,同时也证实了定理的正确性。
文摘On the basis of Thirlwall’s framework (1966),this paper develops a model to analyze the correlation between regional disparities and industry structure.The empirical results show that the differences of industry structure cannot fully account for regional economic disparities.
文摘A systematic approach was presented to develop the empirical model for predicting the ultimate tensile strength of AA5083-H111 aluminum alloy which is widely used in ship building industry by incorporating friction stir welding(FSW) process parameters such as tool rotational speed,welding speed,and axial force.FSW was carried out considering three-factor five-level central composite rotatable design with full replications technique.Response surface methodology(RSM) was applied to developing linear regression model for establishing the relationship between the FSW process parameters and ultimate tensile strength.Analysis of variance(ANOVA) technique was used to check the adequacy of the developed model.The FSW process parameters were also optimized using response surface methodology(RSM) to maximize the ultimate tensile strength.The joint welded at a tool rotational speed of 1 000 r/min,a welding speed of 69 mm/min and an axial force of 1.33 t exhibits higher tensile strength compared with other joints.
