Scatter Diagrams and Regression Lines
Scatter Diagrams
If data is given in pairs then the scatter diagram of the data is just the points plotted on the xyplane. The scatter plot is used to visually identify relationships between the first and the second
e
Sampling and Statistics
Statistics
We start the discussion in the natural way. We all have a general feeling about what statistics is.
In the course of these lecture notes, we will lay out the detail about what statistics is and how it is
used. For now we
Descriptive Statistics and Stem and Leaf Diagrams
Stem and Leaf Diagrams
For data that we want to understand how it looks without losing the individual data points, we
use a stem and leaf diagram. To construct a stem and leaf diagram, we put the first dig
Percentiles and Box Plots
Percentiles
We saw that the median splits the data so that half lies below the median. Often we are
interested in the percent of the data that lies below an observed value.
We call the rth percentile the value such that r percent
Mean, Mode, Median, and Standard
Deviation
The Mean and Mode
The sample mean is the average and is computed as the sum of all the observed outcomes from
the sample divided by the total number of events. We use x as the symbol for the sample mean.
In math
Goodness of Fit
Before the Gondola was in operation, Heavenly tracked its skiers and boarders and found the
following
Type
Beginner
Intermediate
Advanced
Expert
Percent of Skiers
30%
40%
20%
10%
With the new gondola in place the ski resort wants to determ
and for Grouped Data
Calculating the Mean from a Frequency Distribution
Since calculating the mean and standard deviation is tedious, we can save some of this work
when we have a frequency distribution. Suppose we were interested in how many siblings are
Inferences on the Regression Line
Estimating the Mean Value of y for a Particular Value of x
Suppose that you own a pizza restaurant and are interesting in sending out menus to local
residents. You research what your 200 competitors have done to find the
Math 201 Practice Midterm 3
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final answer. Show your work.
Problem 1
A study was done to determine whether LTCC transfer students had a lower retention
Chi Square and Two Way Tables
Two Way Tables
Is there any relationship between political affiliation and the type of car a person drives?
A survey was done and the following data was collected:
Democrat Republican Other Row marginal total
32
15
(24)
(9)
5
Practice Midterm II Key
Problem 1
The South Lake Tahoe Police Department has charted the number of arrests over the past twelve
months. The number of arrests per month that are made follows a Normal distribution with
mean 72 and standard deviation 12. Con
Bar Charts, Frequency Distributions, and Histograms
Frequency Distributions, Bar Graphs, and Circle Graphs
The frequency of a particular event is the number of times that the event occurs.
The relative frequency is the proportion of observed responses in
MATH 201
ELEMENTS of STATISTICS and PROBABILITY
Monday Wednesday and Friday 8:00 to 9:25 AM
Room E100
5 UNITS
Instructor Larry Green
Office Phone Number 541-4660 Extension 341
Internet
Email: [email protected]
Lecture Notes: http:/www.ltcconline.net/greenl/
Correlation
Residuals
Suppose that the average lifespan for people who smoke is:
Packs Per Week
1
2
3
5
Life Span
72
70
69
68
We can calculate the least squares regression line:
y = 73 - 1.3x
We define the first residual to be the difference between the f
ANOVA
ANOVA
We saw that for paired differences we had the hypothesis that
H0: 1 = 2
H1: 1
2
What if there are many types and we want to see if it makes a difference which we look at? We
could test the appropriate hypothesis for each pair, but if we test f
Analyzing the Regression Line
Estimating Sigma
The correlation provides us with an estimate of how linear the data is. We would also like to
know how close the data are to the regression line. We use a measurement se which is a point
estimate for the stan
Math 201 Practice Final
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final answer. Show your work.
Problem 1
Match the following hypotheses and estimates with the appropriate test statistic or con
Test for Homogeneity
Summary: This module describes how the chi-square distribution can be used to test
for homogeneity.
The Goodness of Fit test can be used to decide whether a population fits a given
distribution, but the Goodness of Fit test will not s
Math 201 Practice Midterm I
Please work out each of the given problems. Credit will be based on the steps
that you show towards the final answer. Show your work.
Problem 1 Categorize these measurements associated with Lake Tahoe according to level:
nomina