CH 12
What is the equation that is used for linear regression? HINT: very familar!
y=mx+b
What is the difference between sample and population?
Sample is a certain group of a population.
Population is the entirety of those groups.
The symbol for sample and population mean are...
x̄ & μ
What is the symbol for correlation coefficient and coefficient of determination?
r & r2
What are the two types of data? And which one has two different subgroups and how can we differentiate them?
Qualitative & Quantitative
Quantitative has a Discrete and Continuous Data
The symbol for Sample and Population Standard Deviation is
𝑠 & 𝜎
Imagine a scatter plot where the data points start at the top-left of the graph and trend downward toward the bottom-right. The points are clustered very tightly together, nearly forming a straight line.
a) 0.9
b) 0.4
c) 0
d) -0.4
e) -0.9
e) -0.9
A science class recorded the temperature (in °C) of a liquid every minute during an experiment.
12, 18, 22, 14, 25, 28, 19, 21, 24, 16, 17, 23, 20, 15, 26, 29, 13, 22, 27, 21
Temperature Range Frequency
10 - 14
15 - 19
20 - 24
25 - 29
What are the frequencies for each limit along with the total?
Temperature Range Frequency
10 - 14 3
15 - 19 5
20 - 24 7
25 - 29 5
n= 20
The following dataset represents the scores of 20 students on a recent math certification exam:
52, 55, 60, 64, 68, 70, 72, 75, 78, 80, 82, 85, 86, 88, 90, 92, 95, 96, 98, 100
Find the 33 and 86 percentile.
P86 = 97
A business owner tracks their annual sales (y) starting from year 2 (x). Use your calculator to find the correlation coefficient (r) to three decimal places.
Year (x): Sales (y)
2 22.16
3 24.94
4 23.52
5 21.70
6 20.08
7 18.96
8 20.14
9 20.42
10 19.40
What may r mean?
r= -0.781
the linear trend will be negative and will be a strong linear correlation
Hours per Day Frequency (People)
0–2 62
2–4 55
4–6 31
6–8. 14
8–10 8
10–12 2
Find the Relative Frequency and Cumulative Frequency.
Relative Frequency Cumulative Frequency
62/172 = 0.360 62
55/172 = 0.320 62 + 55 = 117
31/172 = 0.180 117 + 31 = 148
14/172 = 0.0814 148 + 14 = 162
8/172 = 0.0465 162 + 8 = 170
2/172 = 0.0116 170 + 2 = 172
Solve for the population mean, standard deviation and variance. HINT: use your calculators!
34, 42, 28, 37, 40, 31, 45, 33, 39, 36, 41, 30, 29, 38, 44, 32, 35, 40, 27, 43, 31, 34, 39, 36, 42, 28, 35, 41, 33, 37
μ = 36
𝜎 = 5.03
𝜎2= 25.30
A local coffee shop, "The Daily Grind," wants to see if their Instagram ad spending actually helps their monthly revenue. They collected data over the last 5 months:
Ad Spend ( x) Monthly Sales (y)
1.2 15
2.5 22
3.0 21
4.1 30
5.2 34
1) Find the r value (correlation coefficient) interpret what it means.
2) Find the regression equation and solve if x=6.0
1) r = 0.981 ; positive linear trend and a strong linear correlation
2) y^= 4.86x + 8.85
y^= 4.86(6.0) + 8.85 = 38.01
A researcher at the CSUDH College of Business Administration and Public Policy is studying the weekly study hours of 20 undergraduate students. Create a distribution of 5 classes. The raw data for the number of hours spent studying per week is as follows.:
Raw Data (Hours):
12, 15, 18, 22, 25, 25, 28, 30, 32, 35, 35, 38, 40, 42, 45, 48, 50, 52, 55, 58
Solve for the range, class width, and find the classes limits!
range: 58 - 12 = 46
class width: 46/5 = 9.2 = 10
12 - 21
22 - 31
32 - 41
42 - 51
52 - 61
Imagine a teacher records the following test scores for 10 students:
85, 72, 96, 51, 68, 92, 85, 72, 66, 88
What is the 5 number summary of this data? Along with the IQR, lower and upper fence values?
min: 51
Q1: 68
median: 78.5
Q3: 88
max: 96
IQR= 20 ; LF = 38 ; UF = 118