I am doing my masters essay. I am trying to find the determinants of environmental performance index using Human development index as the income variable. I am a bot confused with my results. The EPI and HDI scatter plot showed linear relationship, or it was my mistake, i did not look at it close enough. I already designed all my work around this. I do not have much time in my hand either. Will my OLS regression be legitimate under the cicumstances?
I'm not very familiar with these augmented component-plus-residual plots, but I can't imagine that amount of non-linearity in the model makes the model inappropriate. Nothing is perfect.
Mostafa Rafid Hossain -
I agree with Salvatore that the linearity does not look too bad, IF you stay in this range, but I also have not heard of such an "augmented" plot.
However, the variance is high, and especially if this is only good in this range, then it does not seem to help a great deal with prediction (or explanation either, since you have just one predictor, right?).
If you are using one variable as a predictor, and one as the response, with no intercept term, then that indicates a ratio estimator, and if the relationship is strong, you should have very substantial heteroscedasticity. (See https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR.)
It would be good here for you to show a plot of predictor on the x-axis, and response on the y-axis.
Cheers - Jim
Hello James,
Thanks for the feedback. I am really new at this, never done a research all by my self. rookie you might say. While your paper is very sophisticated, i wont understand much of it. I am not running a simple linear regression. I am trying to find the determinants of Environmental Performance index (EPI). EPI is my dependent variable. Economic growth (HDI), economic structure, trade and government effectiveness, urban pop and pop density are my predictors or independent variables. My data is cross section for 145 countries for the year 2018. I have attached a plot of HDI ( predictor) on the x axis and EPI response on the y axis. Would really like your inputs.
James R Knaub
Mostafa -
There is information there, but it does appear that perhaps the one predictor may not be enough to do the best job you can do. You could do the same kind of plot for each of the other predictors against the same response variable to look for straight or curvilinear (whether technically linear or nonlinear) relationships, and also you could compare the predictors against each other to look for collinearity. (Collinearity can also come from one group of predictors replaceable by another group of either the same or different number of predictors.) The idea being that you could use this graphical study, along with your subject matter knowledge, to decide on the best multiple regression model.
If you research the term "graphical residual analysis" and plot alternative model results on the same scatterplot for the same sample, you can compare the prediction performances for those models, for that sample. However, the idea of a "cross-validation" is that those performances may be quite different for a different sample.
I suggest that you plot data as noted above to see what you can learn about relationships, and considering that, and your subject matter knowledge, construct alternative models, which may consider different predictors, or forms, such as quadratic linear regression, or even just with or without an intercept term, and then compare them using graphical residual analyses and cross-validations.
Subject matter knowledge is important. The graphs can help, but please note that in different combinations with other predictors, the same predictor may behave differently. Once you decide on the model or alternative models you would like to consider, the graphical residual analyses and cross-validations tell you how well it or they perform for prediction.
Best wishes - Jim Knaub
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Regression