# Logarithmic trans guide

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```							Logarithmic Transformations for Exponential and Power Functions
       Starting with a set of data, determine first which is the explanatory and which is response
       Enter Explanatory into L1 and response into L2
       Create a scatterplot with L1 as x and L2 as y
o Is it gently curved (could be power)
o Flat and then sharply curved (could be exponential)
    Check the ratios between each response variable (divide by the prior and then divide by the increment
between x values
o If ratios overall are steadily increasing or decreasing, then power
o If ratios are approximately constant, then exponential

Exponential                           (x,logy)                Power                     (logx,logy)
This is why it works:                                         This is why it works:

(log both sides)                                                 (log both sides)

(apply log rules)                                                (apply log rules)

(LSRL for (x,logy)                                             (LSRL for (logx,logy))

(antilog)                                                      (antilog)

(exponential model)                                             (antilog)

(power model)
This is how to do the process:
This is how to do the process:
       Create L3 by placing cursor at the header and            Create L3 by placing cursor at the header and
keying: log (L2) to fill in the values                    keying: log (L1) to fill in the values. Repeat to
       Perform regression (Stat/Calc/8) for L1, L3, Y1           create L4 using log(L2)
write down the a and b values (to use later)             Perform regression (Stat/Calc/8) for L3, L4, Y1
       Check correlation coefficient (r) to see if strong       Write down a and b values (to use later)
       Make a scatterplot of L1, L3 with LSRL overlay to
   Check correlation coefficient (r) to see if
see if regression worked                                  strong
       Test for linearity with a residual plot                  Make a scatterplot of L3,L4 with LSRL overlay
       Use a = loga and b = logb to write the following          to see if regression worked
equation:                               (step 3          Test for linearity with a residual plot
above)
   Use a = loga and b = b to write the following
       Perform antilog (back-transform) to create the
equation:
exponential model (steps 4 & 5 above)
   Perform antilog (back-transform) to create the
exponential model (steps 4-6 above)

```
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