Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. The table below shows the number of games sold, in thousands, from the years 2000–2010.
Year 2000 2001 2002 2003 2004 2005
Number Sold (thousands) 142 149 154 155 159 161
Year 2006 2007 2008 2009 2010 —
Number Sold (thousands) 163 164 164 166 167 —
A. Let x represent the time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands.
I got log y=141.91242949 + 10.45366573In(x)
D. If you were to manipulate the data you could do the opposite regression of what you did in a) what is this regression formula?
E. Using the regression formula obtained in d) how many games will be sold in 2015? What did you do to the data from the table to obtain this second regression formula?
not quite sure what you're after, but if you rearrange
logy = 141.91242949 + 10.45366573 Inx
you get
lnx = 0.09566022 lny - 13.57537472
That's correct and for E I'm just trying to figure out how many games were sold in 2015 with the rearranged lnx = 0.09566022 lny - 13.57537472 and how did you get to that point?
Oh, please.
If you have y = 3 + 4x
you divide by 4 to get
0.25y = 0.75 + x
and then shift the 0.75
You just have different numbers. Don't forget your Algebra I now that you're studying statistics!
For E, I don't see using any "opposite regression." Your answer for A is used to find the number sold in a given year. x=15 for the year 2015, so just plug it into your equation. Assuming logs base 10, that is
logy = 141.91242949 + 10.45366573 In15
But that is clearly a bad equation, since that gives y=8.438*10^73
That 141.9 is way too big to be a logarithm.
ah. I didn't know you were trying to get exponential.
It looks like you're using logs base 10 as well as base e (lnx). I will assume a typo, and use only natural logs. If you have
lny = a + b lnx
then raise e to the power on both sides
y = e^(a + b lnx)
= e^a * e^(b lnx)
= e^a * (e^ lnx)^b
= e^a * x^b
Now just plug in your numbers.
To find the regression formula for the opposite regression, we need to manipulate the data from regression formula in part (A). The original regression formula is:
log y = 141.91242949 + 10.45366573 * ln(x).
To reverse the regression, we need to solve for x instead of y. Let's start by rewriting the regression formula in its original form:
y = e^(141.91242949) * x^(10.45366573).
Now, let's solve for x:
x = (y / e^(141.91242949))^(1/10.45366573).
To obtain the second regression formula, we manipulated the original regression formula by solving for x instead of y. The formula becomes:
x = (y / e^(141.91242949))^(1/10.45366573).
Now, to find out how many games will be sold in 2015, we need to substitute the value of x with 16 (since 2015 is 16 years from the starting year 2000) into the second regression formula and solve for y:
y = e^(141.91242949) * 16^(10.45366573).
Calculating this equation will give us the estimated number of games sold in 2015.