Linear Regression

Linear Regression Formula

Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data. In some situations, the slope and/or intercept have a scientific meaning. In other cases, you use the linear regression line as a standard curve to find new values of X from Y, or Y from X. A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.

Linear Regression Formula:

Regression Equation(y) = a + bx

Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
Intercept(a) = (ΣY - b(ΣX)) / N


A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Will soon be back with Linear functions and Inequalities.

Arithmetic Progression

Geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. A sequence, such as the numbers 1, 3, 9, 27, 81, in which each term is multiplied by the same factor in order to obtain the following term. Also called geometric sequence. It is a Sequence of numbers where the ratio between any two adjacent numbers is constant.

For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

Progressions and types are different one among them is Arithmetic Progression.

Arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression.

Also you can follow my blogs for Prime factorization. I hope this was useful.

Quadratic Functions

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A quadratic functions, in mathematics, is a polynomial function of the form

ƒ(x) = ax² +bx +c, a≠ 0.

The graph of a quadratic function is a parabola whose major axis is parallel to the y-axis.

Qudratic Functions are presented in three forms namely:-

General form

Factored form

Vertex form or the Standard form

The general technique for graphing quadratic functions is the same as for linear equations graphing However, since quadratics graph as curvy lines (called "parabolas"), rather than the straight lines generated by linear equations, there are some additional considerations.

Graph of quadratic functions are always a parabola either opening upwards or downwards.Also you can follow my blogs for Precalculus Tutorials. I hope this was useful.

TRIGNOMETRY PROBLEMS

What is Trigonometry?

Trigonometry is the branch of mathematics that deals with triangles, circles, oscillations and waves. The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions of angles are the ratio of the various sides of a triangle.

Trigonometry is the science of angular magnitudes and the art of applying the principles of this science to the solution of trigonometry problems. Trigonometry considers the properties of angles and certain ratios associated with angles, and applies the knowledge of these properties to the solution of triangles and various other algebraic and geometric problems. Incidentally trigonometry considers also certain time-saving aids in computation such as logarithms, which are generally employed in the solution of triangles.

Also you can follow my blogs for Trigonometry homework help. I hope this was useful.

DETERMINANTS AND MATRICES

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Today we shall learn about Determinants and Matrices

DETERMINANT

The determinant is a special number associated with any Square Matrix. The fundamental geometric meaning of a determinant is a scale factor for measure when the matrix is regarded as a linear transformation. The determinant of matrices is denoted det(A), or without parentheses: det A. Determinants are mathematical objects that are very useful in the analysis and solution of systems of Linear Equations.

If the matrices determinant is 0, the matrix is said to be singular, and if the determinant is 1, the matrix is said to be unimodular.

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MATRICES

A matrix is simply a set of numbers arranged in a rectangular table. It has 2 rows and 4 columns. We usually write matrices inside parentheses ( ) or brackets [ ]. We can add, subtract and multiply matrices together, under certain conditions. Matrices are used to solve Simultaneous Equations.