I am interested in assessing the trend in new car sales and the factor affecting the sales? GDP, Bank loan issued by the major banks, Consumer Price index, time (in quarters) are considered as independent variables and sales as dependent variable. None of the independent variables are found to be correlated with sales but when Multivariate regression analysis was done, R^2 was 0.99 and significant and showing GDP, Bank Loan and time contributing significantly to the model. How it is possible. Can it be considered as non-linear relationship?
Dear Takiar
Besides your concerns, you may check the collinearity of independent variables. In addition, you may check the forms of variables (such as log or growth rate for more suitable with model).
Best
Canh
Thank you for your response. yes, Collinearity is there. Collinearity may only effect the inclusion or exclusion of certain so called independent variable(s) in the multivariate regression model. Can I frame the question in a different way. If independent variables are not found to be correlated with dependent variable then are we suppose to proceed with the multivariate regression analysis?
Ramnath -
I cannot see how your independent variables could not be correlated with your dependent variable. That seems to be the actual issue. Did you assume they were not correlated because of a p-value in each case? That could be your problem. Isolated p-values, without power or some other sensitivity analysis, are highly misleading.
If you estimate variance of the prediction errors and/or validate findings with separate available test data, that could be more informative for you, but perhaps you do not have enough data?
Residual plots could be very helpful.
Best wishes - Jim
PS - I'm assuming you mean multiple regression, which is not the same as multivariate regression, where you look at multiple dependent variables.
I also suspect that you may not have estimated correlation correctly.
Dear Ramnath
There is a possibility that, the number of observations are less than the number of variables/ parameters in a model, i.e. n
I am using SPSS 21. The bivariate correlations are obtained using the SPSS. The dependent variable chosen are 5 namely GDP, Quarter Value, Bank loans amount issued, Consumer Price Index, Sales vaue. Sales value was found to be only corrleated with sales. All other variable showed non-significant corrleation with sales. But in the model, except bank loan all other variables are shown to be contributing significantly. The No. of observations are 12 that is 4 quarter values for 3 years. According to me it can only happen if there is a exponential or any other relationship between sales and all other variables, which are found to be non-significant. The question remains, if no linear relationship whether those variables should be considered at all for multivariate regression. If yes, how come non-significant correlated variables are figuring in the model as significant contributors?
Dear Sir,
The independent variables may be significant at 10% or higher..
if the data is small and shareable, please share on this platform, so that we will get some idea after looking at the data.
Thanks
Too little data. As I said, p-values are misleading. Change your sample size and you change your p-value.
https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS
Article Practical Interpretation of Hypothesis Tests - letter to the...
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