Homework set 4 - Solutions
|
|
- Angela Kimberly Cannon
- 6 years ago
- Views:
Transcription
1 Homework set 4 - Solutions Math 3200 Renato Feres 1. (Eercise 4.12, page 153) This requires importing the data set for Eercise You may, if you wish, type the data points into a vector. (a) Calculate the five number summary for the daily rainfall data ( min,q 1,Q 2,Q 3, ma ), as well as the IQR, the sample mean, and the sample variance. (b) Obtain a bo-and-whiskers plot for this data. (c) Obtain a stem-and-leaf plot for this data. (d) Obtain a normal plot for this data. Solution. After importing the data file, for which I used the name rain, I assigned it the class matri using rain=data.matri(rain). (a) The summary numbers are: summary(rain) V1 Min. : 452 1st Qu.: 865 Median :1331 Mean :1369 3rd Qu.:1727 Ma. :3830 (b) The bo plot is obtained with the command> boplot(rain,horizontal=true). Notice that I m drawing it horizontally by addinghorizontal=true inside theboplot function (c) For a stem-and-left plot we use stem(rain):
2 > stem(rain) The decimal point is 3 digit(s) to the right of the The stem function takes an additional argument called scale. The default value is scale=1. Higher values can be used to epand the length of the plot. For eample,scale=2 roughly doubles the length of the plot: > stem(rain,scale=2) The decimal point is 2 digit(s) to the right of the (d) For the normal plot: > qqnorm(rain) > qqline(rain) 2
3 This produces the graph: Normal Q Q Plot Sample Quantiles Theoretical Quantiles 2. (Eercise 4.36, page160) This requires importing the data set for Eercise (a) Make a scatter plot of unemployment rate vs. snowfall, with the regression line superimposed. What relationship is indicated by the scatter plot? (b) Find the equation of the regression line. Also find the correlation coefficient. Is there a strong linear relationship between snowfall and unemployment? Solution. After importing the data into R under the name SnowUnemp I converted the data frame into a data matri usingsnowunemp=data.matri(snowunemp). Here is how the matri looks like: > SnowUnemp Year Snow Unemp [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] For convenience I define the vectorssnow=snowunemp[,2] andunemp=snowunemp[,3]. (a) For the scatter plot: > plot(snow,unemp) > lm.unemp=lm(unemp~snow) > lines(snow,fitted(lm.unemp)) 3
4 unemp snow There is a clear correlation between the two variables. As snowfall increases, unemployment increases. (b) To obtain the regression line we invoke thelm function: > lm(formula=unemp~snow) Call: lm(formula = unemp ~ snow) Coefficients: (Intercept) snow The intercept is α= and the regression coefficient is β= So the regression line is Unemployment = Snow The correlation coefficient is > cor(snow,unemp) [1] Recall that this coefficient is at most 1, so the two variables are strongly positively correlated. 3. For each of the following set of computer generated data (, y) obtain a scatter plot showing the regression line and find the correlation coefficient of and y. (For the scatterplot, I suggest using small dots; for eample, plot(,y,ce=0.2,asp=1) should produce a nice enough graph.) (a) = rnorm(200,0,1) y=-+rnorm(200,0,0.8) (b) =rnorm(200,0,1) y=rnorm(200,0,0.8) 4
5 (c) a=2*pi*runif(200,0,1) =cos(a)+rnorm(200,0,0.1) y=sin(a)+rnorm(200,0,0.1) (d) a=2*pi*runif(200,0,1) =2*cos(a)-sin(a)+rnorm(200,0,0.5) y=sin(a)+2*cos(a)+rnorm(200,0,0.5) Solution. The R commands and plot are shown below for each case: (a) > = rnorm(200,0,1) > y=-+rnorm(200,0,0.8) y The correlation coefficient in this case (obtained usingcor(,y)) is: (b) > =rnorm(200,0,1) > y=rnorm(200,0,0.8) The correlation coefficient in this case is: (Close to 0.) (c) > a=2*pi*runif(200,0,1) 5
6 y > =cos(a)+rnorm(200,0,0.1) > y=sin(a)+rnorm(200,0,0.1) y The correlation coefficient in this case is: (Close to 0.) (d) > a=2*pi*runif(200,0,1) > =2*cos(a)-sin(a)+rnorm(200,0,0.5) > y=sin(a)+2*cos(a)+rnorm(200,0,0.5) 6
7 y The correlation coefficient in this case is: (Significant positive correlation.) 4. For each of the data sets (, y) of the previous problem, what linear or quadratic formula would and y satisfy in the absence of random errors? (This is to be done by hand.) Solution. We have, in each case, ignoring the normal random errors in front of and y: (a) = y (b) y = 0 (c) 2 + y 2 = 1 (d) This case requires a little more work. First note that = 2cos a sin a and y = sin a+ 2cos a. Therefore, +y = 4cos a and y = 2sin a and ( +y ) 2+ ( y ) 2= cos 2 a+ sin 2 a= This can be simplified to y+ 5y 2 = 16. 7
Practice in R. 1 Sivan s practice. 2 Hetroskadasticity. January 28, (pdf version)
Practice in R January 28, 2010 (pdf version) 1 Sivan s practice Her practice file should be (here), or check the web for a more useful pointer. 2 Hetroskadasticity ˆ Let s make some hetroskadastic data:
More informationAlgebra 1, 4th 4.5 weeks
The following practice standards will be used throughout 4.5 weeks:. Make sense of problems and persevere in solving them.. Reason abstractly and quantitatively. 3. Construct viable arguments and critique
More informationLINEAR TOPICS Notes and Homework: DUE ON EXAM
NAME CLASS PERIOD LINEAR TOPICS Notes and Homework: DUE ON EXAM VOCABULARY: Make sure ou know the definitions of the terms listed below. These will be covered on the exam. Axis Scatter plot b Slope Coordinate
More informationSTA Module 2B Organizing Data and Comparing Distributions (Part II)
STA 2023 Module 2B Organizing Data and Comparing Distributions (Part II) Learning Objectives Upon completing this module, you should be able to 1 Explain the purpose of a measure of center 2 Obtain and
More informationSTA Learning Objectives. Learning Objectives (cont.) Module 2B Organizing Data and Comparing Distributions (Part II)
STA 2023 Module 2B Organizing Data and Comparing Distributions (Part II) Learning Objectives Upon completing this module, you should be able to 1 Explain the purpose of a measure of center 2 Obtain and
More informationFurther Maths Notes. Common Mistakes. Read the bold words in the exam! Always check data entry. Write equations in terms of variables
Further Maths Notes Common Mistakes Read the bold words in the exam! Always check data entry Remember to interpret data with the multipliers specified (e.g. in thousands) Write equations in terms of variables
More informationa. divided by the. 1) Always round!! a) Even if class width comes out to a, go up one.
Probability and Statistics Chapter 2 Notes I Section 2-1 A Steps to Constructing Frequency Distributions 1 Determine number of (may be given to you) a Should be between and classes 2 Find the Range a The
More informationLinear Topics Notes and Homework DUE ON EXAM DAY. Name: Class period:
Linear Topics Notes and Homework DUE ON EXAM DAY Name: Class period: Absolute Value Axis b Coordinate points Continuous graph Constant Correlation Dependent Variable Direct Variation Discrete graph Domain
More information/4 Directions: Graph the functions, then answer the following question.
1.) Graph y = x. Label the graph. Standard: F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) +k, k f(x), f(kx), and f(x+k), for specific values of k; find the value of k given the graphs.
More information1.3 Graphical Summaries of Data
Arkansas Tech University MATH 3513: Applied Statistics I Dr. Marcel B. Finan 1.3 Graphical Summaries of Data In the previous section we discussed numerical summaries of either a sample or a data. In this
More informationAlgebra 1. 7 th Standard Complete Graphs. Categories Quadratic (p. 3-9) Exponential (p ) Absolute Value (p ) Linear (p.
Algebra 1 7 th Standard Complete Graphs Categories Quadratic (p. -9) Eponential (p. 10-1) Absolute Value (p. 14-17) Linear (p. 18-9) Summative Assessment Date: Wednesda, November 8 th Page 1 Standard:
More informationData Management Project Using Software to Carry Out Data Analysis Tasks
Data Management Project Using Software to Carry Out Data Analysis Tasks This activity involves two parts: Part A deals with finding values for: Mean, Median, Mode, Range, Standard Deviation, Max and Min
More informationDay 4 Percentiles and Box and Whisker.notebook. April 20, 2018
Day 4 Box & Whisker Plots and Percentiles In a previous lesson, we learned that the median divides a set a data into 2 equal parts. Sometimes it is necessary to divide the data into smaller more precise
More informationLearning Log Title: CHAPTER 7: PROPORTIONS AND PERCENTS. Date: Lesson: Chapter 7: Proportions and Percents
Chapter 7: Proportions and Percents CHAPTER 7: PROPORTIONS AND PERCENTS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 7: Proportions and Percents Date: Lesson: Learning Log
More informationPart I, Chapters 4 & 5. Data Tables and Data Analysis Statistics and Figures
Part I, Chapters 4 & 5 Data Tables and Data Analysis Statistics and Figures Descriptive Statistics 1 Are data points clumped? (order variable / exp. variable) Concentrated around one value? Concentrated
More informationIQR = number. summary: largest. = 2. Upper half: Q3 =
Step by step box plot Height in centimeters of players on the 003 Women s Worldd Cup soccer team. 157 1611 163 163 164 165 165 165 168 168 168 170 170 170 171 173 173 175 180 180 Determine the 5 number
More informationCh3 E lement Elemen ar tary Descriptive Descriptiv Statistics
Ch3 Elementary Descriptive Statistics Section 3.1: Elementary Graphical Treatment of Data Before doing ANYTHING with data: Understand the question. An approximate answer to the exact question is always
More informationYear 10 General Mathematics Unit 2
Year 11 General Maths Year 10 General Mathematics Unit 2 Bivariate Data Chapter 4 Chapter Four 1 st Edition 2 nd Edition 2013 4A 1, 2, 3, 4, 6, 7, 8, 9, 10, 11 1, 2, 3, 4, 6, 7, 8, 9, 10, 11 2F (FM) 1,
More informationMath 121 Project 4: Graphs
Math 121 Project 4: Graphs Purpose: To review the types of graphs, and use MS Excel to create them from a dataset. Outline: You will be provided with several datasets and will use MS Excel to create graphs.
More informationSLStats.notebook. January 12, Statistics:
Statistics: 1 2 3 Ways to display data: 4 generic arithmetic mean sample 14A: Opener, #3,4 (Vocabulary, histograms, frequency tables, stem and leaf) 14B.1: #3,5,8,9,11,12,14,15,16 (Mean, median, mode,
More information8.5 Quadratic Functions and Their Graphs
CHAPTER 8 Quadratic Equations and Functions 8. Quadratic Functions and Their Graphs S Graph Quadratic Functions of the Form f = + k. Graph Quadratic Functions of the Form f = - h. Graph Quadratic Functions
More informationEnduring Understandings: Some basic math skills are required to be reviewed in preparation for the course.
Curriculum Map for Functions, Statistics and Trigonometry September 5 Days Targeted NJ Core Curriculum Content Standards: N-Q.1, N-Q.2, N-Q.3, A-CED.1, A-REI.1, A-REI.3 Enduring Understandings: Some basic
More informationChapter 3 - Displaying and Summarizing Quantitative Data
Chapter 3 - Displaying and Summarizing Quantitative Data 3.1 Graphs for Quantitative Data (LABEL GRAPHS) August 25, 2014 Histogram (p. 44) - Graph that uses bars to represent different frequencies or relative
More informationChapter 7: Linear regression
Chapter 7: Linear regression Objective (1) Learn how to model association bet. 2 variables using a straight line (called "linear regression"). (2) Learn to assess the quality of regression models. (3)
More information8 th Grade Pre-Integrated Math
Use order of operations Evaluate expressions Use integers and absolute value Add integers Subtract integers Use inductive reasoning Multiply and divide integers Use properties of numbers Simplify variable
More informationIntegrated Mathematics I Performance Level Descriptors
Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Integrated Mathematics I. A student at this level has an emerging ability to demonstrate
More informationBox and Whisker Plot Review A Five Number Summary. October 16, Box and Whisker Lesson.notebook. Oct 14 5:21 PM. Oct 14 5:21 PM.
Oct 14 5:21 PM Oct 14 5:21 PM Box and Whisker Plot Review A Five Number Summary Activities Practice Labeling Title Page 1 Click on each word to view its definition. Outlier Median Lower Extreme Upper Extreme
More informationRobust Linear Regression (Passing- Bablok Median-Slope)
Chapter 314 Robust Linear Regression (Passing- Bablok Median-Slope) Introduction This procedure performs robust linear regression estimation using the Passing-Bablok (1988) median-slope algorithm. Their
More informationSLOPE A MEASURE OF STEEPNESS through 7.1.5
SLOPE A MEASURE OF STEEPNESS 7.1. through 7.1.5 Students have used the equation = m + b throughout this course to graph lines and describe patterns. When the equation is written in -form, the m is the
More informationVCEasy VISUAL FURTHER MATHS. Overview
VCEasy VISUAL FURTHER MATHS Overview This booklet is a visual overview of the knowledge required for the VCE Year 12 Further Maths examination.! This booklet does not replace any existing resources that
More informationSTA 570 Spring Lecture 5 Tuesday, Feb 1
STA 570 Spring 2011 Lecture 5 Tuesday, Feb 1 Descriptive Statistics Summarizing Univariate Data o Standard Deviation, Empirical Rule, IQR o Boxplots Summarizing Bivariate Data o Contingency Tables o Row
More informationACTIVITY: Representing Data by a Linear Equation
9.2 Lines of Fit How can ou use data to predict an event? ACTIVITY: Representing Data b a Linear Equation Work with a partner. You have been working on a science project for 8 months. Each month, ou measured
More informationSection 4.2 Graphing Lines
Section. Graphing Lines Objectives In this section, ou will learn to: To successfull complete this section, ou need to understand: Identif collinear points. The order of operations (1.) Graph the line
More informationPSY 9556B (Feb 5) Latent Growth Modeling
PSY 9556B (Feb 5) Latent Growth Modeling Fixed and random word confusion Simplest LGM knowing how to calculate dfs How many time points needed? Power, sample size Nonlinear growth quadratic Nonlinear growth
More informationIntegrated Algebra/Geometry 1
*Ability to add, subtract, multiply and divide integers (without the use of a calculator) Ability to make statements about information presented in: tables and graphs concept maps identify and extend patterns
More information2.1: Frequency Distributions and Their Graphs
2.1: Frequency Distributions and Their Graphs Frequency Distribution - way to display data that has many entries - table that shows classes or intervals of data entries and the number of entries in each
More informationCurve Fitting with Linear Models
1-4 1-4 Curve Fitting with Linear Models Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Write the equation of the line passing through each pair of passing points in slope-intercept form. 1.
More information4.1 Graph Quadratic Functions in
4. Graph Quadratic Functions in Standard Form Goal p Graph quadratic functions. Your Notes VOCABULARY Quadratic function Parabola Verte Ais of smmetr Minimum and maimum value PARENT FUNCTION FOR QUADRATIC
More informationMiddle School Math Course 3
Middle School Math Course 3 Correlation of the ALEKS course Middle School Math Course 3 to the Texas Essential Knowledge and Skills (TEKS) for Mathematics Grade 8 (2012) (1) Mathematical process standards.
More informationCASE21 North Carolina Pacing Guide: 8 TH GRADE MATH Updated August 10, 2010
Day Date Unit State Standards Core and Related Concepts 1 N/A Welcome Back Course expectations Math activity 2 Unit 1: 1.05 Integers Integers & (6 th Grade) Compare & order Rational 1.02 Absolute value
More information9.1: GRAPHING QUADRATICS ALGEBRA 1
9.1: GRAPHING QUADRATICS ALGEBRA 1 OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator
More informationRegression Analysis and Linear Regression Models
Regression Analysis and Linear Regression Models University of Trento - FBK 2 March, 2015 (UNITN-FBK) Regression Analysis and Linear Regression Models 2 March, 2015 1 / 33 Relationship between numerical
More informationLesson 2.4 Exercises, pages
Lesson. Eercises, pages 13 10 A 3. Sketch the graph of each function. ( - )( + 1) a) = b) = + 1 ( )( 1) 1 (- + )( - ) - ( )( ) 0 0 The function is undefined when: 1 There is a hole at 1. The function can
More informationChapter 3: Data Description - Part 3. Homework: Exercises 1-21 odd, odd, odd, 107, 109, 118, 119, 120, odd
Chapter 3: Data Description - Part 3 Read: Sections 1 through 5 pp 92-149 Work the following text examples: Section 3.2, 3-1 through 3-17 Section 3.3, 3-22 through 3.28, 3-42 through 3.82 Section 3.4,
More informationIllinois Math Assessment Framework, Grade 7. correlated to
Illinois Math Assessment Framework, Grade 7 correlated to Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write
More informationAppendix 3: PREPARATION & INTERPRETATION OF GRAPHS
Appendi 3: PREPARATION & INTERPRETATION OF GRAPHS All of you should have had some eperience in plotting graphs. Some of you may have done this in the distant past. Some may have done it only in math courses
More informationSubject: Math Models Calendar: Aug-Sept Timeframe: NA Level/Grade: 11-12
Subject: Math Models Calendar: Aug-Sept Timeframe: NA Level/Grade: 11-12 I. Probability a. Define basic probability terms b. Find the probability of Independent event c. Introduce and apply the county
More informationBoxplots. Lecture 17 Section Robb T. Koether. Hampden-Sydney College. Wed, Feb 10, 2010
Boxplots Lecture 17 Section 5.3.3 Robb T. Koether Hampden-Sydney College Wed, Feb 10, 2010 Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, 2010 1 / 34 Outline 1 Boxplots TI-83 Boxplots 2
More informationData Handling. Moving from A to A* Calculate the numbers to be surveyed for a stratified sample (A)
Moving from A to A* A* median, quartiles and interquartile range from a histogram (A*) Draw histograms from frequency tables with unequal class intervals (A) Calculate the numbers to be surveyed for a
More informationChapter 5. Understanding and Comparing Distributions. Copyright 2010, 2007, 2004 Pearson Education, Inc.
Chapter 5 Understanding and Comparing Distributions The Big Picture We can answer much more interesting questions about variables when we compare distributions for different groups. Below is a histogram
More informationCURRICULUM UNIT MAP 1 ST QUARTER
1 ST QUARTER Unit 1: Pre- Algebra Basics I WEEK 1-2 OBJECTIVES Apply properties for operations to positive rational numbers and integers Write products of like bases in exponential form Identify and use
More informationAdvanced Math 8 Friday, January 13, 2017, 4:27PM
Advanced Math 8 Friday, January 13, 2017, 4:27PM Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources Basic Real Number Operation s (Week
More information15 Wyner Statistics Fall 2013
15 Wyner Statistics Fall 2013 CHAPTER THREE: CENTRAL TENDENCY AND VARIATION Summary, Terms, and Objectives The two most important aspects of a numerical data set are its central tendencies and its variation.
More informationCentral Valley School District Math Curriculum Map Grade 8. August - September
August - September Decimals Add, subtract, multiply and/or divide decimals without a calculator (straight computation or word problems) Convert between fractions and decimals ( terminating or repeating
More informationChapter 6: DESCRIPTIVE STATISTICS
Chapter 6: DESCRIPTIVE STATISTICS Random Sampling Numerical Summaries Stem-n-Leaf plots Histograms, and Box plots Time Sequence Plots Normal Probability Plots Sections 6-1 to 6-5, and 6-7 Random Sampling
More informationYear 9 Key Performance Indicators Maths (Number)
Key Performance Indicators Maths (Number) M9.1 N1: I can apply the four operations to negative numbers. Raise negative numbers to a power Add and subtract negative numbers and know when the answer should
More informationEx.1 constructing tables. a) find the joint relative frequency of males who have a bachelors degree.
Two-way Frequency Tables two way frequency table- a table that divides responses into categories. Joint relative frequency- the number of times a specific response is given divided by the sample. Marginal
More informationProject 11 Graphs (Using MS Excel Version )
Project 11 Graphs (Using MS Excel Version 2007-10) Purpose: To review the types of graphs, and use MS Excel 2010 to create them from a dataset. Outline: You will be provided with several datasets and will
More informationScatterplot: The Bridge from Correlation to Regression
Scatterplot: The Bridge from Correlation to Regression We have already seen how a histogram is a useful technique for graphing the distribution of one variable. Here is the histogram depicting the distribution
More informationUnderstanding and Comparing Distributions. Chapter 4
Understanding and Comparing Distributions Chapter 4 Objectives: Boxplot Calculate Outliers Comparing Distributions Timeplot The Big Picture We can answer much more interesting questions about variables
More informationSTA Rev. F Learning Objectives. Learning Objectives (Cont.) Module 3 Descriptive Measures
STA 2023 Module 3 Descriptive Measures Learning Objectives Upon completing this module, you should be able to: 1. Explain the purpose of a measure of center. 2. Obtain and interpret the mean, median, and
More informationSLOPE A MEASURE OF STEEPNESS through 2.1.4
SLOPE A MEASURE OF STEEPNESS 2.1.2 through 2.1.4 Students used the equation = m + b to graph lines and describe patterns in previous courses. Lesson 2.1.1 is a review. When the equation of a line is written
More information3.3 The Five-Number Summary Boxplots
3.3 The Five-Number Summary Boxplots Tom Lewis Fall Term 2009 Tom Lewis () 3.3 The Five-Number Summary Boxplots Fall Term 2009 1 / 9 Outline 1 Quartiles 2 Terminology Tom Lewis () 3.3 The Five-Number Summary
More informationDisplaying Distributions - Quantitative Variables
Displaying Distributions - Quantitative Variables Lecture 13 Sections 4.4.1-4.4.3 Robb T. Koether Hampden-Sydney College Wed, Feb 8, 2012 Robb T. Koether (Hampden-Sydney College)Displaying Distributions
More informationExcel Primer CH141 Fall, 2017
Excel Primer CH141 Fall, 2017 To Start Excel : Click on the Excel icon found in the lower menu dock. Once Excel Workbook Gallery opens double click on Excel Workbook. A blank workbook page should appear
More informationNorth Carolina Standard Course of Study, 2003, grade 8 [NC] PH Course 3 Lesson
[NC] North Carolina Standard Course of Study, 2003, grade 8 PH Course 3 Lesson COMPETENCY GOAL 1: The learner will understand and compute with real 1.01 Develop number sense for the real numbers. 1-2,
More informationR Programming Basics - Useful Builtin Functions for Statistics
R Programming Basics - Useful Builtin Functions for Statistics Vectorized Arithmetic - most arthimetic operations in R work on vectors. Here are a few commonly used summary statistics. testvect = c(1,3,5,2,9,10,7,8,6)
More informationGRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM
FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 1 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM I) THE STANDARD FORM OF A QUADRATIC FUNCTION (PARABOLA) IS = a +b +c. To graph a quadratic function
More informationLesson 17: Modeling with Polynomials An Introduction
: Modeling with Polynomials An Introduction Student Outcomes Students interpret and represent relationships between two types of quantities with polynomial functions. Lesson Notes In this lesson, students
More informationPage 1. Graphical and Numerical Statistics
TOPIC: Description Statistics In this tutorial, we show how to use MINITAB to produce descriptive statistics, both graphical and numerical, for an existing MINITAB dataset. The example data come from Exercise
More informationSimilarities and Differences Or Compare and Contrast
Similarities and Differences Or Compare and Contrast Research has shown that identifying similarities and differences can produce significant gains in student achievement. For it to be effective it must
More informationStatistics Lab #7 ANOVA Part 2 & ANCOVA
Statistics Lab #7 ANOVA Part 2 & ANCOVA PSYCH 710 7 Initialize R Initialize R by entering the following commands at the prompt. You must type the commands exactly as shown. options(contrasts=c("contr.sum","contr.poly")
More informationf( x ), or a solution to the equation f( x) 0. You are already familiar with ways of solving
The Bisection Method and Newton s Method. If f( x ) a function, then a number r for which f( r) 0 is called a zero or a root of the function f( x ), or a solution to the equation f( x) 0. You are already
More informationSolving General Linear Equations w/ Excel
Solving General Linear Equations w/ Ecel Matri Operations in Ecel Ecel has commands for: Multiplication (mmult) matri multiplication Transpose (transpose) transpose a matri Determinant (mdeterm) calc the
More informationSpecial Review Section. Copyright 2014 Pearson Education, Inc.
Special Review Section SRS-1--1 Special Review Section Chapter 1: The Where, Why, and How of Data Collection Chapter 2: Graphs, Charts, and Tables Describing Your Data Chapter 3: Describing Data Using
More informationMuskogee Public Schools Curriculum Map, Math, Grade 8
Muskogee Public Schools Curriculum Map, 2010-2011 Math, Grade 8 The Test Blueprint reflects the degree to which each PASS Standard and Objective is represented on the test. Page1 1 st Nine Standard 1:
More informationBluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition
Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Online Learning Centre Technology Step-by-Step - Minitab Minitab is a statistical software application originally created
More informationAlgebra IA. Unit 1 Connections to Algebra
A Unit 1 Connections to Algebra Time: 20 days Objectives: 1, 2, 8 and 9 Translate verbal into mathematical Write using exponents Use the order of operations to evaluate open sentences by performing arithmetic
More informationThe shortest distance from point K to line is the length of a segment perpendicular to from point K. Draw a perpendicular segment from K to.
8. Find the distance between each pair of parallel lines with the given equations. Copy each figure. Construct the segment that represents the distance indicated. 12. K to The shortest distance from point
More informationLesson 8 - Practice Problems
Lesson 8 - Practice Problems Section 8.1: A Case for the Quadratic Formula 1. For each quadratic equation below, show a graph in the space provided and circle the number and type of solution(s) to that
More informationGRAPHING CALCULATOR REFERENCE BOOK
John T. Baker Middle School GRAPHING CALCULATOR REFERENCE BOOK Name: Teacher: - 1 - To Graph an Equation: Graphing Linear Equations 1.) Press Y= and enter the equation into Y 1. 2.) To see the graph in
More informationCOURSE: Math A 15:1 GRADE LEVEL: 9 th, 10 th & 11 th
COURSE: Math A 15:1 GRADE LEVEL: 9 th, 10 th & 11 th MAIN/GENERAL TOPIC: PROBLEM SOLVING STRATEGIES NUMBER THEORY SUB-TOPIC: ESSENTIAL QUESTIONS: WHAT THE STUDENTS WILL KNOW OR BE ABLE TO DO: Make a chart
More informationMDM 4UI: Unit 8 Day 2: Regression and Correlation
MDM 4UI: Unit 8 Day 2: Regression and Correlation Regression: The process of fitting a line or a curve to a set of data. Coefficient of Correlation(r): This is a value between and allows statisticians
More informationMathematics Year 9-11 Skills and Knowledge Checklist. Name: Class: Set : Premier Date Year 9 MEG :
Personal targets to help me achieve my grade : AFL Sheet Number 1 : Standard Form, Decimals, Fractions and Percentages Standard Form I can write a number as a product of it s prime factors I can use the
More informationCorrelation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11
Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11 1: Number Operations and Concepts Students use numbers, number sense, and number
More informationCAMBRIDGE TECHNOLOGY IN MATHS Year 11 TI-89 User guide
Year 11 TI-89 User guide Page 1 of 17 CAMBRIDGE TECHNOLOGY IN MATHS Year 11 TI-89 User guide CONTENTS Getting started 2 Linear equations and graphs 3 Statistics 5 Sequences 11 Business and related mathematics
More informationAlignment to the Texas Essential Knowledge and Skills Standards
Alignment to the Texas Essential Knowledge and Skills Standards Contents Kindergarten... 2 Level 1... 4 Level 2... 6 Level 3... 8 Level 4... 10 Level 5... 13 Level 6... 16 Level 7... 19 Level 8... 22 High
More informationPrepare a stem-and-leaf graph for the following data. In your final display, you should arrange the leaves for each stem in increasing order.
Chapter 2 2.1 Descriptive Statistics A stem-and-leaf graph, also called a stemplot, allows for a nice overview of quantitative data without losing information on individual observations. It can be a good
More information2.2. Changing One Dimension
2.2 Changing One Dimension The epression (n - 2)(n + 2) is in factored form because it is written as a product of factors. The epression n 2-4 is in epanded form because it is written as the sum or difference
More informationWHOLE NUMBER AND DECIMAL OPERATIONS
WHOLE NUMBER AND DECIMAL OPERATIONS Whole Number Place Value : 5,854,902 = Ten thousands thousands millions Hundred thousands Ten thousands Adding & Subtracting Decimals : Line up the decimals vertically.
More informationThis is called the vertex form of the quadratic equation. To graph the equation
Name Period Date: Topic: 7-5 Graphing ( ) Essential Question: What is the vertex of a parabola, and what is its axis of symmetry? Standard: F-IF.7a Objective: Graph linear and quadratic functions and show
More informationSection 9.3: Functions and their Graphs
Section 9.: Functions and their Graphs Graphs provide a wa of displaing, interpreting, and analzing data in a visual format. In man problems, we will consider two variables. Therefore, we will need to
More informationMiddle School Math 3 and 8th GLEs
Middle School Math 3 and 8th GLEs Chapter. Lesson GLE's Description 1.1 1.2 1.3 1.4 1.5 3.1.1 Use Graphs to analyze data 1.1.6 Order of Operations 1.5.4, 1.5.5(7th) Write and Evalutate Variable Expressions
More informationDr. Junchao Xia Center of Biophysics and Computational Biology. Fall /6/ /13
BIO5312 Biostatistics R Session 02: Graph Plots in R Dr. Junchao Xia Center of Biophysics and Computational Biology Fall 2016 9/6/2016 1 /13 Graphic Methods Graphic methods of displaying data give a quick
More informationSection 4.4: Parabolas
Objective: Graph parabolas using the vertex, x-intercepts, and y-intercept. Just as the graph of a linear equation y mx b can be drawn, the graph of a quadratic equation y ax bx c can be drawn. The graph
More informationMathematics Year 9-11 Skills and Knowledge Checklist. Name: Class: Set : 1 Date Year 9 MEG :
Personal targets to help me achieve my grade : AFL Sheet Number 1 : Standard Form, Decimals, Fractions and Percentages Standard Form I can write a number as a product of it s prime factors I can use the
More informationNUMBER 1 ALGEBRA 1 AUTUMN TERM YEAR 7
NUMBER 1 Know what even numbers, odd numbers, factors, multiples, primes, squares and square roots are and how to find them. Find the Highest Common Factor by listing factors and/or using Venn diagrams.
More informationSurvey of Math: Excel Spreadsheet Guide (for Excel 2016) Page 1 of 9
Survey of Math: Excel Spreadsheet Guide (for Excel 2016) Page 1 of 9 Contents 1 Introduction to Using Excel Spreadsheets 2 1.1 A Serious Note About Data Security.................................... 2 1.2
More informationApplied Regression Modeling: A Business Approach
i Applied Regression Modeling: A Business Approach Computer software help: SAS SAS (originally Statistical Analysis Software ) is a commercial statistical software package based on a powerful programming
More informationLearning Log Title: CHAPTER 8: STATISTICS AND MULTIPLICATION EQUATIONS. Date: Lesson: Chapter 8: Statistics and Multiplication Equations
Chapter 8: Statistics and Multiplication Equations CHAPTER 8: STATISTICS AND MULTIPLICATION EQUATIONS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 8: Statistics and Multiplication
More information