Data Transformation

'data.frame':	150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa
[1] 3.325508 3.325508 3.325508 3.325508 3.325508 3.177822

Call:
lm(formula = Sepal.Width^Trans ~ Petal.Width)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.43393 -0.08438 -0.00148  0.08841  0.40230 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.00987    0.02294  87.619  < 2e-16 ***
Petal.Width -0.07501    0.01616  -4.642 7.54e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1503 on 148 degrees of freedom
Multiple R-squared:  0.1271,	Adjusted R-squared:  0.1212 
F-statistic: 21.55 on 1 and 148 DF,  p-value: 7.54e-06