Question

The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. X 0 1 2 3 4 5 y 2. 82 3. 29 3. 46 3. 33 2. 88 2. 24 a. Y = negative 0. 143 x squared 0. 595 x 2. 830 c. Y = negative 0. 143 x squared 0. 595 x minus 2. 829 b. Y = 0. 143 x squared 0. 596 x 2. 829 d. Y = 0. 143 x squared minus 0. 595 x 2. 830.

Answer 1

The quadratic regression equation for this data set is $\rm y=-0.143x^2+0.59x+2.82$.

What is the general form of a quadratic equation?

The general form of the quadratic equation is given by;

$\rm ax^2+bx+c=0$

Where; a, b, and c are the constants.

x;   0       1         2        3          4         5

y;  2.82  3. 29  3. 46  3. 33   2. 88  2. 24

From the table when the value of x = 0 the value of y is 2.82.

Then,

$\rm y=ax^2+bx+c\\\\x=0\\\\2.82=a0^2+b(0)+c\\\\c=2.82$

From the table when the value of x = 3 the value of y is 3.33.

$\rm y=ax^2+bx+c\\\\x=3\\\\2.82=a(3)^2+b(3)+c\\\\9a+3b+2.82=2.82\\\\9a=-3b\\\\b=-3a$

From the table when the value of x = 5 the value of y is 2.24.

$\rm y=ax^2+bx+c\\\\x=3\\\\2.24=a(5)^2+(-3a)(5)+c\\\\25a-15a+2.82=2.24\\\\40a=2.24-2.82\\\\10a=-0.68\\\\a= \dfrac{-0.68}{10}\\\\a=-0.143$

And the value of b is;

$\rm b=3a\\\\b=3(-0.14)\\\\b=0.59$

Therefore,

The quadratic regression equation for this data set is;

$\rm y=ax^2+bx+c\\\\y=-0.143x^2+0.59x+2.82$

Hence, the quadratic regression equation for this data set is $\rm y=-0.143x^2+0.59x+2.82$.

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