# Plotting linear regression with factors

I'm working on a project with R and I don't think I'm using the appropriate linear regression or plot, I've made both but they don't seem to match. The study is an ANOVA comparing $CO_2$ emissions per capita with 5 groups of income levels and a relevant linear regression. For the linear regression I want use $CO_2$ as the dependent variable and $GDP$ as the independent variable and the 5 $income$ levels as dummy variables.

Begin by ordering the variables and remove the intercept:

income_factor = factor(Data01$income, levels=c("Low income", "Lower middle income", "Upper middle income", "High income: OECD", "High income: nonOECD")) lm.r = lm(CO2 ~ income_factor -1, data=Data01)  Gives summary(lm.r) Coefficients: Estimate Std. Error t value Pr(>|t|) income_factorLow income 0.2318 0.6943 0.334 0.73902 income_factorLower middle income 1.7727 0.6355 2.789 0.00603 ** income_factorUpper middle income 4.7685 0.6271 7.604 4.12e-12 *** income_factorHigh income: OECD 8.7926 0.7305 12.036 < 2e-16 *** income_factorHigh income: nonOECD 19.4642 1.3667 14.242 < 2e-16 ***  So that we may write the linear regression in the form: $$CO_2 = \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4 + \beta_5 X_5$$ Where$X_i$is a dummy variable 1 at the level of income and 0 otherwise For the corresponding plot I used:  plot <- ggplot(data=Data01, aes(x=GDP, y=CO2, colour=factor(income))) plot + stat_smooth(method=lm, fullrange=FALSE) + geom_point()  Which gives the graph But here is my confusion, it looks like there is the lm term in the plot, but I don't think it is using the same values taken from the previous linear regression. As Looking at summary from the linear regression, High income: OECD the estimate is 8.79, but the line for it is pretty much flat. While I was typing this I realized that the graph has$GDP$as the X-axis, but is not included in the linear regression. Would multiplying by$income$_$factor*GDP\$ help?

If the income factors are based on GDP per capita, GDP basically equals $$income factor \times population$$ Your results would be much clearer if you could run the regression with population instead of GDP. Then the interaction variables income_factor*population would make a lot of sense.