Regression with indexes in R

Question

I am trying to estimate tax elasticity with OLS. Below you can see example of my dataset.

dataset<-data.frame(
              gross_income_new=c(5000,4000,3000,2000,1500,200,1000,200,1500),
              gross_income_old=c(4500,3900,2100,1500,1450,210,980,100,1200),
              tax_burden=c(10,10,9,8,7,10,10,8,8),
              tax_burden1=c(17,11,12,14,15,14,12,17,15),
              gross_income_index=c(90,97.5,70,75,97,105,98,50,80),
              tax_burden_Index=c(170,110,133,175,214,140,120,213,188))
            
    
    Elasticity = lm(log(gross_income_index)~log(tax_burden_Index), data = dataset) 
    summary(Elasticity)

And this is results from regression.

Call:
lm(formula = log(gross_income_index) ~ log(tax_burden_Index), 
    data = dataset)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.36995 -0.05404  0.04150  0.11507  0.29487 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)   
(Intercept)             6.7252     1.6104   4.176  0.00416 **
log(tax_burden_Index)  -0.4557     0.3176  -1.435  0.19447   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2197 on 7 degrees of freedom
Multiple R-squared:  0.2273,    Adjusted R-squared:  0.1169 
F-statistic: 2.059 on 1 and 7 DF,  p-value: 0.1945

So for this example first I converted data into indexes, convert in logs an after that I estimate elasticity which is -0.4557 %.

Now I want to make prediction into sample for column gross_income_new in order to see how my model works. Here I want to emphasize that I want to try this only with coefficient of elasticity (not with regression equation). In order to do that I try with this equation but I am little bit confused because I worked in indices and now I need to estimate values in different normal values not indexes. So I try with formula

Prediction=(gross_income_old) + (tax_burden-tax_burden1)*elasticity

But obviously I made same mistakes and result are not good. So can anybody help me how to solve this problem ?

score 0 · Answer 1 · answered Jan 29 '22 at 11:21

Using the formula you suggested, this is what I get:

library(dplyr)
dataset <- dataset %>% 
  mutate(Prediction = gross_income_old + (tax_burden - tax_burden1)*coef(Elasticity)[2])
dataset
#   gross_income_new gross_income_old tax_burden tax_burden1 gross_income_index tax_burden_Index Prediction
# 1             5000             4500         10          17               90.0              170  4503.1901
# 2             4000             3900         10          11               97.5              110  3900.4557
# 3             3000             2100          9          12               70.0              133  2101.3672
# 4             2000             1500          8          14               75.0              175  1502.7344
# 5             1500             1450          7          15               97.0              214  1453.6458
# 6              200              210         10          14              105.0              140   211.8229
# 7             1000              980         10          12               98.0              120   980.9115
# 8              200              100          8          17               50.0              213   104.1015
# 9             1500             1200          8          15               80.0              188  1203.1901

But I am not sure does this approach is correct ? I also got these results. Any opinion ? — silent_hunter, Jan 29 '22 at 11:37
Whether this is an appropriate way to generate a prediction is more of a statistics question and less of an R question. Perhaps you'd be better served by asking on CrossValidates. — DaveArmstrong, Jan 29 '22 at 19:33

Regression with indexes in R

1 Answers1