MATH 100 Flashcards
Least Square Regression Line Equation
y = a + (b)(x)
[(-) if b is negative]
Predicted Score (outcome)
Dependent Variable
y
the y-intercept
a
The Slope of the Line
b
Independent Variable
(controlled-manipulated-change) explanatory
x
Regression Table
x I y I x2 I y2 I xy
Formula of a
a= (y)(x2) – (x) (xy)
——————————
N (x2) – (x)2
Formula of b
b= N (XY) - (X) (Y)
—————————
N (X2) - (X)2
The degree that describes the relationship between two sets of variables.
Correlation
The strength of a correlation is measured by?
Correlation Coefficient R
other term for R
Pearson Product Moment Correlation
Who developed Pearson Product Correlation?
Carl Pearson
Equation of r
r= (n(Σxy)-(Σx)(Σy))
____________________________________
(√[n[(Σx^2 )-(∑x)^2][n(Σy^2 )-(Σy)^2])
Correlation ranges from
-1 to 1 only
0.00 to +/- 0.19
No correlation exist
+/-0.20 to +/- 0.39
Slight correlation exist
+/- 0.40 to +/- 0.59
Substantial correlation exist
+/- 0.60 to +/- 0.79
Significant correlation exist
+/- 0.80 to +/- 0.99
Very significant correlation exist
+/- 1
Perfect correlation exist
to estimate roughly the relationship existing between two variables, by drawing a straight line intersecting as many points as possible in the graph.
The Scatterpoint Diagram
Positive Correlation / direct relationship
left to right (upwards)
*some positive - if scattered
Negative Correlation/ inverse relationship
left to right (downwards)
*some negative - if scattered
Zero Correlation/no relationship
scattered left and right (magulo)
the rate of revenues received for every dollar on invested in an item or activity
ROI
An instrument that signifies ownership in a corporation and represents a claim on a share of a corporation’s assets and profits. Typically riskier and long-term investments.
Stock
An instrument that signifies ownership in a corporation and represents claim on a share of a corporation’s assets and profits. Stocks are typically riskier and long-term investments. Low risk
Bonds
State law requires corporations pay bond payments on time, a given priority over other financial obligations
Corporate Bonds
Very safe, high quality
Government Bonds
Tax-free on interest for federal returns!!
Lower interest rates, but good overall returns due to tax-exempt status
Municipal Bonds
Are open-ended investments that are professionally managed and consist of a variety of investment instruments including stocks, bonds, options, commodities, and money market securities. Long gterm.
Mutual Funds
A piece of land and any buildings or structures on it. Real estate is a long-term investment.
Real estate
The cost of credit on a yearly basis as a percentage rate.
Annual Percentage Rate (APR)
A form of security to help guarantee that a creditor will be repaid.
Collateral
A legal agreement to receive cash, goods, or services now and pay for them in the future.
Credit
The 3 C’s of Credit:
- Capacity
- Capital
- Character
A type of interest that is paid only on the original amount deposit
and not on past interest paid.
Simple Interest
Simple Interest
I = Prt
A = P+I = P(1 + rt)
Time of Simple interest
T = I/PR
Principal
P = I/RT
Rate
R = I/PT
Interest on Interest
Compounding Interest
Compounding Interest Formula
F=P*(1+i)^n
- n is number of years
Compounding Interest Time Formula
t = Log10 (A/P)
————————
n Log10 (1+ r/n)
method of paying a loan (principal and interest) on installment basis, usually of equal amounts at regular intervals
Amortization Method
a loan, secured by collateral, that the borrower is obliged to pay at specified terms
Mortgage
Find the mortgage
down payment = (down payment rate) (cash price)
mortgage amount/amount of loan
= (cash price) - (down payment)
Alternate solution for mortgage
mortgage amount = % of financed amount x value of the property
= (.100 - %) (value of property)
a system of arithmetic for integers, where numbers “wrap around” upon reaching a certain value—the modulus (plural moduli)
modular arithmetic
Who developed the modular arithmetic?
Carl Friedrich Gauss
Properties of modular arithmetic
[(a mod n) + (b mod n)] mod n = (a + b) mod n
[(a mod n) - (b mod n)] mod n = (a - b) mod n
[(a mod n) x (b mod n)] mod n = (a x b) mod n
Examples
- 11 mod 8 = 3; 15 mod 8 = 7
[(11 mod 8 ) + (15 mod 8)] mod 8 = 10 mod 8 = 2
(11 + 15) mod 8 = 26 mod 8 = 2 - [(11 mod 8 ) - (15 mod 8)] mod 8 = -4 mod 8 = 4
(11 - 15) mod 8 = -4 mod 8 = 4 - [(11 mod 8 ) x (15 mod 8)] mod 8= 165 mod 8 = 5
(11 x 15) mod 8 = 165 mod 8 = 5
How to solve for mod
Ex: 3 mod 7
= 3/7 = 0.4285
= .4285 x 7 (get only the decimals)
in a stage of an algortithm
Ex: 39*15 mod 11
39 mod 11 = 6 and 15 mod 11 = 4
6x4 mod 11 = 24 mod 11
(repeat until the least value)
the study of methods for sending secret messages
Cryptography
to convert the ciphertext back into plaintext
decryption
a message, called plaintext, is converted into a form, called ciphertext
encryption
an algorithm for performing encryption or decryption— a series of well-defined steps that can be followed as a procedure
Cipher
encryption or decryption using Caesar Cipher
C = (M+ shift) mod 26
encrypt = +
decrypt = -
numeric equivalents
A = 0 onwards
An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:
< : less than
≤ : less than or equal to
> : greater than
≥ : greater than or equal to
Graphing rules:
<
≤
>
≥
< Left - open
≤ Left - closed
> Right - open
≥ Right - closed
inequality by subtraction
solve for
X-15<73
x < 88
If (-) = add
inequality by addition
y+15<25
y < 10
If (+) = subtract
inequality by multiplication
x/5 = 10
5 (x/5) = 10x5
x = 50
inequality by division
5x > 20
5x/5 > 20/5
x> 4
when solving a negative number
flip the sign
x+6 ≤ 7
3 ≤ x-5
-3x ≥ -15
x-9 > -5
- x ≤ 1
- 8 ≤ x or x ≥ 8
- x ≤ 5
- x > 4
greater than/less than
dotted line
greater than/less than/equal to
solid line
greater than or greater than, equal to
Shade Above the Line
less than or less than, equal to
Shade below the line
