Disclaimer: I am a senior undergraduate student of Political Science with little proficiency in Data Science; please help me understand better and forgive any ensuing statistical illiteracy!
TL;DR: I created an OLS regression model using appropriate variable selection methods—wherein I reduced seventeen predictor variables to seven. Now, I am illustrating my OLS assumptions w.r.t to this model and asking for help in creating a better model.
I employed OLS Regression in order to study the correlation between my dependent variable of Infant Mortality Rate (per 1000 live births) with respect to the following predictor variables: (1) Mothers received Antenatal care (%); (2) Mothers received Financial Assistance under JSY Scheme (%); (3) Average expenditure at a public health facility(Rs.); (4) Adult Female Literate (%); (5) Per capita NSDP (Rs.); (6) Households with Sanitation (%); (7) Households with Electricity (%).
I am studying this in the context of the Indian nation-state; therefore, my samples—or—N = 32 (the Indian States and UTs excluding those for whom no information was made available).
When I ran a linear multiple OLS Regression on this model (unweighted and not generalized), I obtained the following vital information:
- Residual Standard Error: 7.529 on 24 Degrees of Freedom
- Multiple R-squared: 0.7324
- Adjusted R-squared: 0.6543
- F-statistic: 9.384 on 7 and 24 DF
- p-value: 1.397e-05
Using the sjmisc and sjPlot packages, I ran the following code to test my OLS assumptions:
require(sjmisc) require(sjPlot) plot_model(Model1, type = "diag")
I am sharing the results of the assumptions.
Based on the assumption and regression results, do you all think that I am on the right track at all? From what I could gather, I can obviously see some issues of (1) non-normal distribution of residuals and (2) heteroscedasticity. However, do you all think that my assumptions of multicollinearity and non-normality of residuals and outliers (Q-Q) are alright?
More importantly, how do I fix these issues and attempt to create a better second model? Please consider that I am a relative beginner to the whole process, so forgive me for not knowing the proper direction. Is my preliminary regression model and result even decent? If so, how should I further improve (1) the normality of my residuals; (2) homoscedasticity; (3) regression results?
Lastly, are there any problems in the way I tested my OLS assumptions?
Thank you so much for your time. Have a great day!