# 统计学

Ques-4。c:为了我们的分析,我们已经6个独立变量。Model-1代表利润的比例这6个独立变量而model-2和model-3使用“现金流作为%的销售额”&“营业”。Ques-7:改善这些模型的解释力,无关紧要的变量应该被删除。删除这些变量将改进模型或解释的权力不会有任何影响。从上面给出的表,可以删除变量CLTR和列弗改善模型。。Ques-8:以利润为因变量,以下共线性统计得到:以上共线性统计表明,只有dimension-7条件指数大于15。这个维度对应尺寸变量的方差比例是0.5以上,表明多重共线性可能是一个问题。宽容和方差膨胀因子(VIF)分别从0.316 – 0.819和0.316 – 3.165为给定的回归模型。这表明共线性回归模型没有有害的。Ques-1:Non-stationarity使用单元测试方法在时间序列数据可以发现,空的假设是存在单位根。拒绝假说表明固定数据集和失败拒绝无效假设表明数据非平稳。对于非平稳数据转化为静止的,我们可以使用差分算子或自然对数。差分算子——时间序列是differenced使用差分算子,直到它变得平稳。使用差分算子的数学表达是:ΔYt =次- Yt-1。重复这个过程,直到我们获得固定数据。自然对数——自然对数柔滑,减少异常值的影响。数学是表示为ΔYt = ln(次/ Yt-1)。普通最小二乘法给出了合适的结果当时间序列数据是固定的。OLS估计结果无效的非平稳数据使用。这是由于使用非平稳数据可能导致相关的不相关的变量似乎是有高度统计学意义。因此,这种情况下会产生无效的估计。

Ques-4.c: For the purpose of our analysis, we have taken 6 independent variables. Model-1 represents Profit margin as a percentage of these 6 independent variables whereas model-2 and model-3 use ‘cash-flow as % of sales’ & ‘EBIDTA’ respectively. Ques-7: To improve explanatory power of these models, insignificant variables should be removed. Removing these variables will either improves the model or won’t have any impact on explanatory powers. As clear from the table given above, variables CLTR and LEV can be removed to improve the models. .Ques-8: By taking Profit Margin as the dependent variable, the following collinearity statistics are obtained:Above collinearity statistics shows that only dimension-7 has condition index greater than 15. Variance proportion for this dimension corresponding to SIZE variable is above 0.5 which indicates multicollinearity might be an issue.Tolerance and Variance Inflation Factor (VIF) vary from 0.316 – 0.819 and 1.197 – 3.165 respectively for the given regression model. This indicates that regression model does not have harmful collinearity.Ques-1: Non-stationarity in time-series data can be identified using unit test method where null hypothesis is that unit root is present. Rejection of hypothesis indicates stationary data set and failure to reject null hypothesis indicates that data is non-stationary.For converting non-stationary data into stationary, we can use either difference operator or natural logarithm. Difference operator – Time series is differenced using difference operator until it becomes stationary. Use of difference operator is expressed mathematically as: ΔYt = Yt – Yt-1. The process is repeated until we get stationary data.Natural Logarithm – Natural logarithm smoothens and reduces the impact of outliers. Mathematically it is represented as ΔYt = ln (Yt / Yt-1). Ordinary least square method gives suitable results when time-series data is stationary. OLS results in invalid estimates in case non-stationary data is used. This is because of use of non-stationary data may result in unrelated variables seeming to be related with a high degree of statistical significance. Thus, this situation will produce invalid estimates.