Transcript Linear and Quadratic Regression

arithmetic Sequence: A sequence of numbers where
the common difference occurs at level D1
Given the terms of a sequence.
The first term, t1, is referred to as a. The common
difference is referred to as d.
1. To determine the common difference, d, subtract
backwards.
2. To determine the equation or formula for a sequence
of numbers, determine a and d, and substitute into
the general formula,
tn  a  (n  1)d
Given two non-consecutive terms.
3. To determine the equation or formula if given only
two terms.
Use tn and n to substitute into the general formula
to create two linear equations.
Solve the system of equations to determine a and d.
4. To determine the value of x if three algebraic terms
are provided.
Subtract backwards to find the two algebraic forms
of D1.
Equate the two differences and then solve for x.
Using the TI Calculator.
Linear Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
5
4
7
5
9
Using the calculator to determine the equation
1. First reset your calculator.
Press 2nd, +, Reset, All Ram, Enter, Reset, Enter.
2. Turn Diagnostics ON. This will determine the
percentage of fit.
Press 2nd , 0, arrow down to Diagnostics ON, Enter,
Enter.
Using the TI Calculator.
Linear Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
5
4
7
5
9
3. Press Stat, Enter. Enter term #’s in List 1. Arrow over to List 2 and
enter Term Values.
Using the TI Calculator.
Linear Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
5
4
7
5
9
4. Press Stat. Arrow over to Calc. Scroll down to Lin Reg (ax+b). Hit
ENTER.
So, the equation of the sequence is
t n  2n  1
100%
match
Q
4
3
2
1
−6
−4
−2−1
−2
−3
−4
y
adratic Sequence: A sequence of numbers
x
2
4
6
where the common difference occurs at level D2
Given the terms of a sequence.
The power of the sequence is 2.
1. To determine the common difference, d, subtract
backwards.
2. The general formula for the nth term of a Quadratic
2
Sequence is
t n  an  bn  c
3. To determine the equation or formula for a quadratic
sequence, use the following formulas.
D2  2a
3a  b  1st term in D1
a  b  c  1st term in Sequence
Given non-consecutive terms.
3. What if n doesn’t increase by just 1 unit?
e.g.
Term #
Number
2
2
4
8
6
22
8
44
10
74
Let’s go back to the algebraic determination of the relationship between
2
D2 and “a”.
t2  a(2)  b(2)  c  4a  2b  c
t4  a(4) 2  b(4)  c  16a  4b  c
t6  a(6) 2  b(6)  c  36a  6b  c
SEQUENCE
4a  2b  c, 16a  4b  c,
12a  2b
36a  6b  c
20a  2b
8a
In this case,
D2  8a  (22 ) * 2a  (inc 2 ) * 2a
12a+2b= 1st term in D1 and 4a+2b+c= 1st term in sequence.
Using the TI Calculator.
Quadratic Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
6
4
10
5
15
Using the calculator to determine the equation
1. First reset your calculator.
Press 2nd, +, Reset, All Ram, Enter, Reset, Enter.
2. Turn Diagnostics ON. This will determine the
percentage of fit.
Press 2nd , 0, arrow down to Diagnostics ON, Enter,
Enter.
Using the TI Calculator.
Linear Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
6
4
10
5
15
3. Press Stat, Enter. Enter term #’s in List 1. Arrow over to List 2 and
enter Term Values.
Using the TI Calculator.
Linear Regression: The process of determining the
line of best fit.
Term #
Number
1
1
2
3
3
6
4
10
5
15
4. Press Stat. Arrow over to Calc. Scroll down to Quad Reg. Hit
ENTER.
100%
match
So, the equation of the sequence is
tn 
1 2 1
n  n
2
2