I have a multiple linear regression model which should explain the variation store price elasticities using consumer characteristics of the market area surrounding a store. Therefore, my dependent variable are 74 different PE. My independent variables are income (log median income), education level, elderly and household size. The problem I am dealing with is that income and PE show a non-linear (parabolic) relationship in my category (beer).
The values of income range from 9.8 to 11.2. Now my professor gave me two options:
Tranform the variable (square)
demoreg <- lm(pe ~ squaredincome + income + educ + hhlarge + age60, data = demo) summary(demoreg)
I feel like there is a mistake but how can I interpret the income coefficient(s)?
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 64.588934 34.506386 1.872 0.065735 sqincome 0.569562 0.315751 1.804 0.075892 income -12.437625 6.592960 -1.887 0.063696 educ 0.019858 0.005524 3.595 0.000626 hhlarge -0.029244 0.013254 -2.207 0.030886 age60 0.012861 0.005902 2.179 0.032947 Residual standard error: 0.2441 on 65 degrees of freedom Multiple R-squared: 0.5755, Adjusted R-squared: 0.5428 F-statistic: 17.62 on 5 and 65 DF, p-value: 5.376e-11
Option: Create two variables one for all income levels that show a negative relationship and one for all income levels that show a positive relationship so I get two coefficients that show how much the PE changes if the median income changes 1%.
PE = β0 + β1* income_low + β2* income_high
As the low is at 10.6, I created a dummy variable:
data$dummylow <- ifelse(data$income <= 10.6,1,0) data$dummyhigh <- ifelse(data$income >10.6,1,0) data$low <- ifelse(data$dummylow ==1, demo_clean$income, NA) #$ data$high <- ifelse(data$dummyhigh ==1, demo_clean$income, NA)
If I include now both variables in the regression equation I get the error code:
demoreg <- lm(pe ~ low + high + educ + hhlarge + age60, data = demo) lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) All cases NA
I want to include both variables in the equation as I need two coefficients, but I don't know how to do it.