Question

the average number of cars entering a shopping center parking lot is collected and shown in the table below.
find the quadratic model of the data set provided. round to the nearest thousandth.
model: y = type your answer... x² + type your answer... x + type your answer...

Explanation:

Step1: Input data into calculator

Using a graphing calculator or statistical software, input the time values (20, 60, 100, 140, 180, 220, 240) as \(x\) - values and the car - count values (70, 178, 260, 301, 284, 260, 195) as \(y\) - values.

Step2: Perform quadratic regression

On the calculator, select the quadratic regression function (\(y = ax^{2}+bx + c\)). The calculator will calculate the coefficients \(a\), \(b\), and \(c\) based on the least - squares method.
For a set of data points \((x_i,y_i)\) with \(i = 1,\cdots,n\), the quadratic regression formula minimizes the sum \(S=\sum_{i = 1}^{n}(y_i-(ax_{i}^{2}+bx_{i}+c))^{2}\).
After performing the regression on the given data:
\(a=-0.006\), \(b = 1.736\), \(c = 37.929\)

Answer:

\(y=-0.006x^{2}+1.736x + 37.929\)