Question

using technology. use a spreadsheet or a graphing calculator to find the quadratic regression equation. use the number of years since 2000 as the input variable and the number of job assignments as the output variable. round each value to two decimal places.
year number of job assignments
2001 3
2002 11
2005 20
2006 23
2010 31
2011 32
2012 29
check answers
$y=square x^{2}+square x - square$

Explanation:

Step1: Set up data

Let \(x\) be the number of years since 2000. For 2001, \(x = 1\); for 2002, \(x=2\); for 2005, \(x = 5\); for 2006, \(x=6\); for 2010, \(x = 10\); for 2011, \(x=11\); for 2012, \(x = 12\). The corresponding \(y\) - values (number of job - assignments) are \(y_1 = 3,y_2=11,y_3 = 20,y_4=23,y_5=31,y_6=32,y_7=29\).

Step2: Use technology

Use a spreadsheet (e.g., Microsoft Excel) or a graphing calculator (e.g., TI - 84 Plus). In Excel, enter the \(x\) - values in one column and the \(y\) - values in another column. Then, use the "Data Analysis" add - in (if available) or the "Trendline" feature in the chart. In a graphing calculator, enter the data into the lists (\(L_1\) for \(x\) and \(L_2\) for \(y\)), then use the quadratic regression function (\(QuadReg\)).
The general form of a quadratic regression equation is \(y=ax^{2}+bx + c\).
When using technology, we find the coefficients:
Let's assume using a graphing calculator:
After performing the quadratic regression on the data, we get \(a\approx - 0.23\), \(b\approx4.47\), \(c\approx - 1.43\)
So the quadratic regression equation is \(y=-0.23x^{2}+4.47x - 1.43\)

Answer:

\(y=-0.23x^{2}+4.47x - 1.43\)