AP Statistics 2017

(Marvins-Underground-K-12) #1
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 .
Free download pdf