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Marina86 [1]
4 years ago
10

Which equation is the quadratic regression equation for the data shown in the table?

Mathematics
1 answer:
Leona [35]4 years ago
7 0

<u>Answer-</u>

Quadratic regression equation  y=0.392x^2 - 5.583x + 21.167}

<u>Solution-</u>

Quadratic Regression  Equation,

ax^2+bx+c

a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}

b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}

c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}

Where,


\sum xx=\sum x^2-\frac{(\sum x)^2}{n}

\sum xy=\sum xy-\frac{\sum x\sum y}{n}

\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}

\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}

\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}

Calculating the values from the table,

a= 0.392

b= -5.583

c= 21.167

∴ Quadratic regression equation,

y=0.392x^2 - 5.583x + 21.167


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