Is the textbook wrong?

[Seige]

Hey guys, so I'm studying from the maths quest textbook and I came across this question:

2) Age group (years)    |    9  |   10  |   11  |  12  |  13  |  14  |  15  |  16  |  17  |  18  |
    Average height (cm) | 128 | 144  |  148 | 154 | 158 | 161 | 165 | 164 | 166 | 167 |

The original linear regression line yielded :
                                               Height = 3.76*age + 104.7, with r=0.92

a) Plot the original data and regression line
c) Apply a log₁₀(x) transformation
b) Perform a regression analysis on the transformed data and comment on your result.
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This question was easy enough, I plotted the original data and got the same regression equation as the one given.
BUT I applied a log transformation to the 'x' values and ended up with this regression equation.
                                                Height =  117.17*age + 24.26

at first I thought, oh yeah that must be the answer but then I looked at the next question which continues from this question (not 'c' but question 3).

3) "Use the transformed data from question 2 to predict the heights of girls of the following ages:
i 7 years old
ii 10.5 years old
iii 20 years old

So I got my transformed regression line and plugged in '7' where age was but ended up with a height of 844.45! I mean seriously! What kind of girl, or human being at that matter can be that tall! I did everything the question asked, I applied a log transformation to the x variables and used those variables plus the unchanged 'y' variables to form a new equation and then predicted the height from it. I did this question about 6 times so its not like I am accidently pressing the wrong numbers or anything. PLEASE HELP! I AM SO CONFUSED! Is there something I am missing or is this question wrong?

thanks!

[Sanguinne]

this is from memory so it might be wrong.

you have to log the 7 as the x undergoes a log transformation.

after that, you sub in the log7 and you should get a reasonable answer.

[Zealous]

this is from memory so it might be wrong.

you have to log the 7 as the x undergoes a log transformation.

after that, you sub in the log7 and you should get a reasonable answer.

Sanguinne is right.

You've applied a log transformation to the x values, so you must put in a log(x) in the place of the x in the regression equation in order to sort of "counteract" the modification of x values you did before.

So the regression equation is "Height = 117.17 x log(age) +24.26"

[MagicGecko]

The above comments are correct. These are the type of questions that VCAA will use to trick students, so be sure not to fall for it again

[plato]

So I got my transformed regression line and plugged in '7' where age was but ended up with a height of 844.45!

Looking at the given table, if someone says they are definitely that tall, you can call them an "out and out liar".