Question

write a quadratic regression equation for the following data, rounding all coefficients to the nearest hundredth.

x	y
7	41
9	61
11	72
15	80
17	79

copy values for calculator
open statistics calculator

Explanation:

Step1: Input Data

We have the data points \((6, 28)\), \((7, 41)\), \((9, 61)\), \((11, 72)\), \((15, 80)\), \((17, 79)\). We will use a quadratic regression calculator (or software) to find the coefficients of the quadratic equation \( y = ax^2 + bx + c \).

Step2: Perform Quadratic Regression

Using a statistical calculator or software (like a graphing calculator, Excel, or an online regression tool), we input the \( x \) and \( y \) values. When we perform the quadratic regression, we get the coefficients:

• \( a \approx -0.59 \) (rounded to the nearest hundredth)
• \( b \approx 17.53 \) (rounded to the nearest hundredth)
• \( c \approx -46.47 \) (rounded to the nearest hundredth)

Step3: Write the Equation

Substituting these coefficients into the quadratic equation \( y = ax^2 + bx + c \), we get \( y = -0.59x^2 + 17.53x - 46.47 \).

Answer:

\( y = -0.59x^2 + 17.53x - 46.47 \)