Download 4 2 + - Tate County School District

Solution
Name ____________________________
Block _____ Date ________
Algebra: 6.2.2 Correlation Coefficient
Bell Work: Graph each system using intercepts and label the solution to each system on its graph.
a.
𝑥−𝑦=4
2𝑥 + 𝑦 = 2
x y
4 0
0 -4
x y
1 0
0 2
8
−3𝑥 + 𝑦 = 3
y
6
4
2
x
−8
−6
−4
−2
8
b. 3𝑥 − 2𝑦 = 6
2
4
6
8
−2
Solution: (𝟐, −𝟐)
−4
−6
−8
x y
-1 0
0 3
y
6
4
2
x
−8
−6
−4
x y
2 0
0 -3
Solution: (−𝟒, −𝟗)
−2
2
−2
−4
−6
−8
6-67. CORRELATION COEFFICIENT
a.
b.
What happens to r as the points get closer to the line of best fit?
The value of 𝒓 approaches 1 (or negative 1) as the points get closer to the line of best fit
What is the largest r that is possible? The smallest?
The largest value is 1. The smallest value is -1
c.
d.
Can r be negative? Can r be zero? What does that mean?
Yes. Yes. If 𝑟 = 0 the trend line is horizontal and the points are scattered
What does r reveal about the strength of the linear association?
If 𝑟 is close to 1 or - 1 the association is strong.
If 𝑟 is far from 1 or -1 the association is weak.
6-68. Write down the following calculator keystrokes
a.
Where do you enter data into the calculator (L1, L2)?
Stat, Enter
b.
What two things must you do to see a graph of data in (L1, L2)?
Turn on the plot and adjust the window
c.
How do you turn on diagnostics?
2nd 0 and scroll down to Diagnostics On.
4
6
8
6-69. The following scatterplots have correlation r = −0.9, r = −0.6, r = 0.1, and r = 0.6. Which scatterplot has
which correlation coefficient, r?
a.
b.
c.
d.
6-70. Graph the system
3𝑥 − 2𝑦 ≤ 6
𝑥 + 4𝑦 > 4
8
y
6
4
2
x
−8
−6
−4
−2
2
4
6
−2
−4
−6
−8
6-71. Write each equation in vertex form:
a. 𝑦 = 2𝑥 2 − 4𝑥 + 7
𝑦 = 2(𝑥 − 1)2 + 5
b. 𝑦 = −𝑥 2 + 4𝑥 − 5
𝑦 = −(𝑥 − 2)2 − 1
8
6-72. Solve by factoring: 3𝑥 + 𝑥 2 = 5
𝑥 2 + 3𝑥 − 5 = 0
Prime – cannot be solved by factoring.
6-73. Sam collected data in problem 6-4 by measuring the pencils of her classmates. She recorded the length of
the painted part of each pencil and its weight. Her data is listed in the table below.
a. What is the equation of the LSRL?
b. The teacher’s pencil, when it was new, had 16.8 cm of paint
and weighed 6g. What was the residual?
c. What does a positive residual mean in this context?
6-74. Solve each equation. (Check by graphing)
a.
6(2x – 5) = – (x + 4)
b.
12𝑥 − 30 = −𝑥 − 4
𝑥 2 − 6𝑥 − 7 = 𝑥 2 + 2𝑥 − 3
13𝑥 − 30 = −4
−6𝑥 − 7 = 2𝑥 − 3
13𝑥 = 26
−8𝑥 − 7 = −3
𝒙=𝟐
−8𝑥 = 4
6-75. Simplify each expression using positive exponents only.
a.
(x + 1)(x – 7) = (x – 1)(x + 3)
b.
(6x3)(3xy)–1
𝑥=
4
𝟏
=−
−8
𝟐
c.
6-76. During a two-month period gasoline increased from $4.10 per gallon to $4.35 per gallon. Assuming
prices increased in a geometric sequence, what was the monthly multiplier and what was the percent increase?
PARCC PREP
I.
II.
𝑦=
Δ𝑦 −32.5 + 29.5 −3
=
=
Δ𝑥
22 − 20
2
𝑦 = 𝑚𝑚 + 𝑏
−31 =
−3
𝑥 + 0.5
2
x y
1 -1
3 -4
−3
(21) + 𝑏
2
−31 = −31.5 + 𝑏
0.5 = 𝑏
III.
0.5 𝑓𝑓
4𝑓𝑓 2
Δ𝑦 0.5
=
= 0.125
Δ𝑥
4