Question

the temperature at various times on a summer day at a resort in southern california is given in the following table.
find the quadratic model of the data set provided. round to four (4) decimals places as necessary (some may not go 4 places and that is okay).
model: ( y = - 0.0007 ) type your answer... ( x ^ { 2 } + ) type your answer... ( x + ) type your answer...

Explanation:

Step1: Input data into calculator

Input the time values (20, 80, 160, 240, 320, 400) as \(x\) - values and temperature values (59, 71, 81, 86, 86, 80) as \(y\) - values into a graphing calculator or statistical software.

Step2: Use quadratic regression function

On a TI - 84 Plus (or similar calculator), go to STAT > CALC > QuadReg. The calculator will calculate the quadratic regression equation of the form \(y = ax^{2}+bx + c\).
When we perform the quadratic regression on the given data:
The quadratic regression formula is \(y=-0.0007x^{2}+0.4175x + 40.0714\)

Answer:

\(y=-0.0007x^{2}+0.4175x + 40.0714\)