The scatterplot of Hours versus ln (Number ) and the residual plot for ln ( ) = –0.0047 +
0.586(Hours ) are as follows:The scatterplot looks much more linear, and the residual plot no longer has the distinctive pattern of
the raw data. We have transformed the original data in such a way that the transformed data is well
modeled by a line. The regression equation for the transformed data is: ln ( ) = –0.047 +
0.586(Hours ).
The question asked for how many bacteria are predicted to be present after 3.75 hours. Plugging 3.75
into the regression equation, we have ln ( ) = –0.0048 + 0.586(3.75) = 2.19. But that is ln (
), not . We must back-transform this answer to the original units. Doing so, we have
= e 2.19 = 8.94 thousand bacteria.
Calculator Tip: You do not need to take logarithms by hand in the above example—your calculator is
happy to do it for you. Simply put the Hours data in L1 and the Number data in L2 . Then let L3 =
LN(L2). The LSRL for the transformed data is then found by LinReg(a +bx) L1,L3,Y1 .
Remember that the easiest way to find the value of a number substituted into the regression
equation is to simply find Y1(#) . Y1 is found by entering VARS Y-VARS Function Y1 .