Chapter 13 Outside of the normal

About ranks, transformations, …

Hooker and Yule paper, 1906

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## 
## Call:
## lm(formula = diff(export) ~ diff(production) + diff(price), data = Wheat_export)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -438894 -139590   39148  188279  303853 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      4.301e+04  7.106e+04   0.605 0.557241    
## diff(production) 3.051e-01  5.672e-02   5.379 0.000224 ***
## diff(price)      6.404e+04  1.792e+04   3.574 0.004362 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 259500 on 11 degrees of freedom
## Multiple R-squared:  0.8176, Adjusted R-squared:  0.7844 
## F-statistic: 24.65 on 2 and 11 DF,  p-value: 8.629e-05

They computed indices, which seem to be the standardized annual differences.

## 
## Call:
## lm(formula = export ~ price + production, data = Indices)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.78544 -0.24981  0.07006  0.33694  0.54378 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.083e-17  1.241e-01   0.000 1.000000    
## price       4.665e-01  1.305e-01   3.574 0.004362 ** 
## production  7.021e-01  1.305e-01   5.379 0.000224 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4643 on 11 degrees of freedom
## Multiple R-squared:  0.8176, Adjusted R-squared:  0.7844 
## F-statistic: 24.65 on 2 and 11 DF,  p-value: 8.629e-05

What if we do it with log proportional change …

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## [1] 0.740655

## 
## Call:
## lm(formula = delta_export ~ delta_price + delta_production, data = Deltas)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.03150 -0.75490 -0.02567  1.22324  2.56527 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)       -0.1720     0.4365  -0.394  0.70114   
## delta_price        0.3642     3.2910   0.111  0.91387   
## delta_production   7.8920     2.1741   3.630  0.00396 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.607 on 11 degrees of freedom
## Multiple R-squared:  0.5491, Adjusted R-squared:  0.4671 
## F-statistic: 6.697 on 2 and 11 DF,  p-value: 0.01252