Question

regents exam questions s.id.b 6: regression 4
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6 the table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through
1994
using ( x = 1 ) to represent the year 1986 and ( y ) to represent the number of new stores, write the exponential
regression equation for these data. round all values to the nearest thousandth.

Explanation:

Step1: Input data into calculator

Enter \(x = 1\) (for 1986), \(x = 2\) (for 1987), \(\cdots\), \(x = 9\) (for 1994) and corresponding \(y\) values (14, 27, 48, 80, 110, 153, 261, 403, 681) into a graphing calculator or statistical software.

Step2: Perform exponential regression

Use the exponential regression function (\(y = ab^{x}\)) on the calculator. The calculator will calculate the values of \(a\) and \(b\).
After performing the regression, we get \(a\approx7.517\) and \(b\approx1.599\)

Answer:

\(y = 7.517\times1.599^{x}\)