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Standard IX

Mathematics

Linear Equation in Two Variables

The normal eq...

Question

The normal equation for the line of best fit for regression analysis of two vaiables $x, y$ are

\sum y = n c + m \sum x

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\sum y = m x + c

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y = m x + c

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y = m \sum x + c

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Solution

The correct option is A $\sum y = n c + m \sum x$
The normal equation for line of best fit regression analysis of two variable $x, y$ are
$\sum y = n c + m \sum x$
$y -$ Regression or Dependent Variable or Explained Variable
$x -$ Independent Variable or Predictor or Explanator
The two constants $c$ and $m$ are regression parameters.

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Similar questions

Q. Given data

x	1	3	4	6
y	1	2	4	4

Find the value of

m

and

c

for the equations of the lines of best fit for the regression analysis between

x a n d y

What does the "c" in the equation y = mx + c, stand for? Where x, y are variables and m, c are constants.

The differential equation for the line y=mx+c is (where c is arbitrary constant)

Q. Find the line of best fit for the following data, treating x as dependent variable (Regression equation

x

y

$X$	14	12	13	14	16	10	13	12
$Y$	14	23	17	24	18	25	23	24

Hence, estimate the value of

x

when

y = 16

A straight line is said to be an asymptote to the curve y=f(x) if the

⊥

distance of point P(x, y) on the curve from the line tends to zero when

x \to \infty

y \to \infty

or both x & y

\to \infty

(a) Asymptotes parallel to y-axis:

The line

x = k

is asymptote to the curve y=f(x) If

{lim}_{x \to k^{+}} f (x) = \infty

- \infty

{lim}_{x \to k^{-}} f (x) = + \infty

- \infty

b) Asymptotes parallel to x-axis:

The line

y = k

is asymptotes to the curve

y = f (x)

{lim}_{x \to \infty} y = k

{lim}_{x \to - \infty} y = k

Let y=mx+c be an asymptote of the curve y=f(x), then from any point P(x, y) on the curve, the

⊥

distance is

\frac{| y - m x - c |}{\sqrt{1 + m^{2}}}

which

\to 0

as x tends to

+ \infty

+ \infty

Thus

y - m x - c \to 0

x \to + \infty

- \infty

Again

y - m x - c = x (\frac{y}{x} - \frac{c}{x} - m) = 0

x \to \infty

and

y - m x - c \to 0

lim x \to \pm \infty (\frac{y}{x} - \frac{c}{x} - m) = 0

\Rightarrow

lim x \to \pm \infty \frac{y}{x} = m

and

{lim}_{x \to \pm \infty} y - m x - c = 0

\Rightarrow

{lim}_{x \to \pm \infty} y - m x = c

So we come to the fact that if y=mx+c is an asymptote to the curve y=f(x). Then as

x \to + \infty

- \infty

{lim}_{x \to \infty} \frac{y}{x} = m = {lim}_{x \to \infty} \frac{f (x)}{x}

{lim}_{x \to \infty} = y - m x = {lim}_{x \to \infty} {f (x) - m x} = c

On the basis of above information answer the following questions. The vertical & horizontal asymptotes to the curve

y = \frac{e^{x}}{x}

are respectively

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The normal equation for the line of best fit for regression analysis of two vaiables x,y are

The correct option is A ∑y=nc+m∑xThe normal equation for line of best fit regression analysis of two variable x,y are∑y=nc+m∑xy– Regression or Dependent Variable or Explained Variablex– Independent Variable or Predictor or ExplanatorThe two constants c and m are regression parameters.

The normal equation for the line of best fit for regression analysis of two vaiables $x, y$ are