Statistical Methods for Data Reduction and Classification
Linear Regression
Linear Regression: Finds the best line that summarizes the relationship between two variables. (Imagine a bunch of dots and a line representing the relationship).
Dimensionality Reduction
A large number of variables results in a dispersion matrix that is too large to study. Dimensionality reduction reduces the number of variables to a few. Why?
- Simpler Analysis: Fewer features make it easier to find patterns.
- Faster Processing (e.g., Trading).
- Better Visualization: It’s easier to visualize
Essential Geometric Definitions and Theorems
Angles and Lines
- Acute Angle: An angle that measures less than 90º.
- Angles: Formed by two rays that share a common endpoint, provided that the two rays are non-collinear.
- Angle Bisector: A ray that contains the vertex and divides the angle into two congruent angles.
- Complementary Angle: A pair of angles that sum 90º.
- Congruent Angles: Two angles are congruent if and only if they have equal measure.
- Corresponding Angles: Angles that are created at the same location at each intersection where a transversal
Understanding Vector Spaces, Linear Algebra, Eigenvalues, and Quadratic Forms
A.1.7. Vector Subspaces
A subset H of a vector space V is a vector subspace if and only if:
- The zero vector 0 is in H.
- For any vectors v1 and v2 in H, their sum v1 + v2 is also in H.
- For any vector v1 in H and any scalar k, the scalar multiple k*v1 is also in H.
Examples of non-vector subspaces:
- Sets defined by polynomial equations.
- Vectors u = (x, y) where xy + x = 0.
- Logarithmic functions.
Examples of vector subspaces:
- Sets defined by linear equations like Ax + By + Cz = 0.
- Sets defined by linear equations
Understanding Floating-Point Representation and Errors
Floating-Point Representation and Errors
t: precision – a positive integer
β: base (or radix) – an integer ≥ 2 (2, 10, 16)
e: exponent – an integer
(decimal) value d1.d2d3 · · · dt × β -> (d1 + d2/β1 + · · · + dt/βt-1 ) × βe
exponent range emin ≤ e ≤ emax
1 + 2*((B -1)B(t-1) * (emax- emin + 1)) norm
1 + 2 * (Bt * (emax – emin + 1)) denorm
Memory stored in 3 fields: sign (1 bit positive negative), exponent (depends on range), fraction or significant (depends on precision)
1 + EpsM
Read MoreKey Marketing Research Variables and Editing
Scales of Measurement in Marketing Research
Understanding different scales is crucial for accurate data interpretation.
- Nominal Scale: Numbers serve only as labels or tags for identifying and classifying objects. In marketing research, it’s used to identify respondents, brands, attributes, and other objects. Example: Numbers assigned to runners in a race.
- Ordinal Scale: Indicates rank order, providing directional information in addition to nominal information. It measures non-numeric concepts like
Statistics and Sampling: True or False Practice Questions
1) A population is a set that includes all elements about which we wish to draw a conclusion. True
2) If we examine some of the population measurements, we are conducting a census of the population. False. Example: A census is defined as examining all of the population measurements.
3) A random sample is selected so that every element in the population has the same chance of being included in the sample. True
4) An example of a quantitative variable is the manufacturer of a car. False
5) An example
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