Difference between revisions of "Manuals/calci/INTERCEPT"

Revision as of 23:57, 18 December 2013

INTERCEPT(y,x)

This function is calculating the point where the line is intesecting y-axis using dependent and independent variables.
Using this function we can find the value of $y$ when $x$ is zero.
The intercept point is finding using simple linear regression.
It is fits a straight line through the set of $n$ points in such a way that makes vertical distances between the points of the data set and the fitted line as small as possible.
Regression methods nearly to the simple ordinary least squares also exist.
i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope

and intercept which provides a solvable pair of equations called normal equations.

Suppose there are $n$ data points ${y_{i},x_{i}}$ , where i = 1, 2, …, n.
To find the equation of the regression line: $a=bar{y}-b.bar{x}$ .
This equation will give a "best" fit for the data points.
The "best" means least-squares method. Here b is the slope.
The slope is calculated by: $b={\frac {\sum _{i=1}^{n}{(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}}{\sum _{i=1}^{n}{(x_{i}-bar{x})}^{2}}}$ .
In this formula $bar{x}$ and $bar{y}$ are the sample means AVERAGE of $x$ and $y$ .
In $INTERCEPT(y,x)$ , the arguments can be numbers, names, arrays, or references that contain numbers.
The arrays values are disregarded when it is contains text, logical values or empty cells.
This function will return the result as error when any one of the argument is nonnueric or x and y is having different number of data points and there is no data.

INTERCEPT(Y,X)

Where Y is the dependent set of observations or data, and

Y is the independent set of observations or data.

This function calculates the point at which a line will intersect the y-axis using the available x-values and y-values.

· An array contains text, logical values, or empty cells that are ignored; but, the cells with the value zero are included.

· INTERCEPT shows the error value, when Y and X have a dissimilar number of data points.

Formulas:-

· The equation to calculate the intercept of the regression line, a, is:

where b is the slope, and is calculated as:

and where x and y are the sample means AVERAGE(Y) and AVERAGE(X).

INTERCEPT

Lets see an example,

INTERCEPT(Y, X)

B C

10 13

8 11

15 18

6 12

12 10

=INTERCEPT(B2:B6,C2:C6) is 1.2268

Syntax

Remarks

Examples

Description

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 and intercept which provides a solvable pair of equations called normal equations.
 *Suppose there are <math> n </math> data points  <math> {y_{i}, x_{i}}</math>, where i = 1, 2, …, n.
-*To find the equation of the regression line:<math> a=bar(y)-b.bar(x)</math>.
+*To find the equation of the regression line:<math> a=bar{y}-b.bar{x}</math>.
 *This equation will give a "best" fit for the data points.
 *The "best" means least-squares method. Here b is the slope.
-*The slope is calculated by:<math> b=\frac{\sum_{i=1}^{n} {(x_{i}-\bar(x))(y_{i}-\bar(y))}} {\sum_{i=1}^{n}{(x_{i}-bar(x))}^2}</math>.
+*The slope is calculated by:<math> b=\frac{\sum_{i=1}^{n} {(x_{i}-\bar{x})(y_{i}-\bar{y})}} {\sum_{i=1}^{n}{(x_{i}-bar{x})}^2}</math>.
-*In this formula<math> bar(x)</math> and<math> bar(y)</math> are the sample means  AVERAGE of <math> x</math>  and <math> y </math>.
+*In this formula<math> bar{x}</math> and<math> bar{y}</math> are the sample means  AVERAGE of <math> x</math>  and <math> y </math>.
 *In <math>INTERCEPT(y,x)</math> , the arguments can be numbers, names, arrays, or references that contain numbers.
 * The arrays  values are  disregarded when it is contains text, logical values or empty cells.