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?
To obtain the regression formula for part D, you need to perform the opposite of the regression used in part A. In part A, you transformed the data by taking the logarithm of the number of games sold. To reverse this transformation, you will need to apply the inverse function, which is the exponentiation function.
The reverse regression formula will be in the form of y = a * e^(bx), where e is the mathematical constant approximately equal to 2.71828.
To find the coefficients a and b for the reverse regression, you can use the coefficients obtained in part A. In part A, the equation was log y = 141.91242949 + 10.45366573 * In(x).
To obtain the reverse regression formula, you will use the fact that y = e^(log y).
Therefore, the reverse regression formula will be:
y = e^(141.91242949 + 10.45366573 * In(x))
Now, for part E, to estimate the number of games sold in 2015 using the obtained regression formula, substitute the value of x corresponding to the year 2015 into the formula. In this case, x = 2015 - 2000 + 1 = 16.
So, substitute x = 16 into the reverse regression formula:
y = e^(141.91242949 + 10.45366573 * In(16))
Calculating this expression will give you the estimated number of games sold in 2015.