title: Regression with indexes in R
body: <p>I am trying to estimate tax elasticity with OLS. Below you can see example of my dataset.</p>
  <pre><code>dataset&lt;-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) 
  </code></pre>
  <p>And this is results from regression.</p>
  <pre><code>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(&gt;|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
  </code></pre>
  <p>So for this example first I converted data into indexes, convert in logs an after that I estimate elasticity which is  -0.4557 %.</p>
  <p>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</p>
  <pre><code>Prediction=(gross_income_old) + (tax_burden-tax_burden1)*elasticity
  </code></pre>
  <p>But obviously I made same mistakes and result are not good. So can anybody help me how to solve this problem ?</p>