Math 52 Linear Regression Instructions TI-83
|
|
- Prudence Melanie Welch
- 6 years ago
- Views:
Transcription
1 Math 5 Linear Regression Instructions TI-83 Use the following data to study the relationship between average hours spent per week studying and overall QPA. The idea behind linear regression is to determine if two variables have a linear relationship, and to find the equation of a line that best fits the data. Th first question is - does the data appear to have a linear relationship? A scatterplot of the data usually helps determine if a relationship appears to exist. If the relationship appears to be linear you will want to determine the line of best fit and the correlation coefficient. Eyeballing the data usually is useless as far as determining the linearity of the data, some kind of scatterplot is your best bet. Average Weekly Study Hours = AWSH AWSH G.P.A DRAW A SCATTERPLOT You can either draw a scatterplot by hand or use your calculator. Enter the data into your calculator as you normally would, except now you have to enter the x values into one list and the y values into another list. Put the x s into L1 and the y s into L. 1
2 The easiest way to plot the data using the calculator is to do the following: 1. Turn the STAT plot on, do this by pressing [ nd ] and [Y=] to get the following: You will need to activate the plot, activate PLOT 1 by pressing [1] or [Enter] to get First use the blue arrow keys to highlight the On choice (once the cursor in on the ON choice press [ENTER] to activate it). Second you need to pick the scatterplot choice from the list of choices, it is the first choice. Third enter the lists your x and y values are entered into (for our example this is L1 and L) Finally press the blue [Graph] key. Note: if your graph does not appear, press the blue [ZOOM] and scroll down until you see the choice 9:ZoomStat, this will readjust the window dimensions and most likely you will see the graph now.. CALCULATE r (the CORRELATION COEFFICIENT) To get the summary statistics for calculating the value of r (the correlation coefficient), run the -var stats for x and y. -var stats can be found in the same menu as 1-var stats, it is the second choice, that is:
3 Pressing [ENTER] will yield: scrolling through the list will yield We can calculate the value of r by using r = = n ( x)( y) n y ( x ) ( x) ( ) ( y) n 78.8 xy ( )( ) =.658 = 1 1( 35.4) ( 76)( 33.5) ( 684.5) 76 1( ) 33.5 We can also get the calculator to calculate r for us. Under the TESTS menu (you can find this menu under the main STATS menu). Scroll down to find choice E, 3
4 Pick choice E and the screen should change to Note: 1. The x and y list should correspond to the lists where you entered your data, so here it should be L1 and L.. The Freq choice will usually be For the β & ρ : 0 <0 >0 row highlight the 0 choice. 4. Next to the RegEq we want to enter Y 1, to do so, place the cursor next to the RegEq and then press [VARS], move the cursor to highlight the Y-Vars menu, the first choice should be 1:Function, press 1 or [ENTER], the new menu should yield a list of y-vars, the first choice should be 1:Y 1, just press [ENTER] and you should return to the line RegEq and the Y 1 should be where you want it (you should not have to do this step again unless you erase the calculator memory). The screen should now look like : Now put the cursor on the Calculate choice and press enter, you should get the following: 4
5 scroll down to get the rest of the information More information is given than we need at the moment, but we will go back and use the rest, notice the value for r is the same was we calculated by hand. 3. TEST r FOR STATISTICAL SIGNIFICANCE Once r is calculated, we need to determine if r is statistically significant. If r is statistically significant then we will proceed to find the regression line (or line of best fit). There are two ways to test the significance of r. This test involves testing H o : ρ = 0 there is no significance H 1 : ρ 0 there is a significant relationship Method 1 Using Table A-6 1. Find the absolute value of r. Determine your level of significance, either 0.05 or Go to the row that corresponds to n 4. If the absolute value of your r is greater than the value from the table, your r is statistically significant, and there is a linear correlation. Method Using the t-test for r. 5
6 r 1. Calculate t =, the degrees of freedom are n- 1 r n. Find the t-statistic from Table A-3, row n- and the column that corresponds to your choice of α. 3. Determine if your test statistic falls in the rejection or acceptance region. (Notice the t value is calculated when you run the LinRegTTest as well as the p-value for the test) If r is statistically significant, we can proceed and find the line of best fit. 4. FIND REGRESSION LINE (or LINE OF BEST FIT) We have already found all the info we need to calculate the line of best fit when we found the -var stats. The line of best fit has the form ˆ = b + b x, where y ( y)( x ) ( x)( n( x ) ( x) xy b = = y-intercept and 1 ( xy) ( x)( y) n( x ) ( x) n b = = slope In this case we can find that ( 33.5)( 684.5) ( 76)( 35.4) b = = 1( 684.5) ( 76) 438 1( 35.4) ( 76)( 33.5) 78.8 b 1 = = ( 684.5) ( 76) = ) So our line of best fit is yˆ = x Notice the calculator calculated these values when we ran the LinRegTTest, note on the calculator b 0 is the value of a and b 1 is the value of b. Graph the line of best fit over the scatterplot of the data set and see that we have 6
7 To get the line in your graph, just press the blue [GRAPH] key again, and the scatterplot should appear but this time the regression line should also appear (this results because you entered the Y 1 next to the RegEQ in the LinRegTTest, if you had not done this the line would not appear now). 7
Session 4 2:40 3:30. If neither the first nor second differences repeat, we need to try another
Linear Quadratics & Exponentials using Tables We can classify a table of values as belonging to a particular family of functions based on the math operations found on any calculator. First differences
More informationIntermediate Algebra Summary - Part I
Intermediate Algebra Summary - Part I This is an overview of the key ideas we have discussed during the first part of this course. You may find this summary useful as a study aid, but remember that the
More informationdetermine whether or not this relationship is.
Section 9-1 Correlation A correlation is a between two. The data can be represented by ordered pairs (x,y) where x is the (or ) variable and y is the (or ) variable. There are several types of correlations
More informationMINI LESSON. Lesson 2a Linear Functions and Applications
MINI LESSON Lesson 2a Linear Functions and Applications Lesson Objectives: 1. Compute AVERAGE RATE OF CHANGE 2. Explain the meaning of AVERAGE RATE OF CHANGE as it relates to a given situation 3. Interpret
More informationChapter 12 : Linear Correlation and Linear Regression
Chapter 1 : Linear Correlation and Linear Regression Determining whether a linear relationship exists between two quantitative variables, and modeling the relationship with a line, if the linear relationship
More informationOverview. 4.1 Tables and Graphs for the Relationship Between Two Variables. 4.2 Introduction to Correlation. 4.3 Introduction to Regression 3.
3.1-1 Overview 4.1 Tables and Graphs for the Relationship Between Two Variables 4.2 Introduction to Correlation 4.3 Introduction to Regression 3.1-2 4.1 Tables and Graphs for the Relationship Between Two
More informationChapter 12: Linear Regression and Correlation
Chapter 12: Linear Regression and Correlation Linear Equations Linear regression for two variables is based on a linear equation with one independent variable. It has the form: y = a + bx where a and b
More informationIntroductory Statistics
Introductory Statistics This document is attributed to Barbara Illowsky and Susan Dean Chapter 12 Open Assembly Edition Open Assembly editions of open textbooks are disaggregated versions designed to facilitate
More informationCh Inference for Linear Regression
Ch. 12-1 Inference for Linear Regression ACT = 6.71 + 5.17(GPA) For every increase of 1 in GPA, we predict the ACT score to increase by 5.17. population regression line β (true slope) μ y = α + βx mean
More information10.1 Simple Linear Regression
10.1 Simple Linear Regression Ulrich Hoensch Tuesday, December 1, 2009 The Simple Linear Regression Model We have two quantitative random variables X (the explanatory variable) and Y (the response variable).
More informationSection 2.2: LINEAR REGRESSION
Section 2.2: LINEAR REGRESSION OBJECTIVES Be able to fit a regression line to a scatterplot. Find and interpret correlation coefficients. Make predictions based on lines of best fit. Key Terms line of
More informationUsing a graphic display calculator
12 Using a graphic display calculator CHAPTER OBJECTIVES: This chapter shows you how to use your graphic display calculator (GDC) to solve the different types of problems that you will meet in your course.
More informationLesson 4 Linear Functions and Applications
In this lesson, we take a close look at Linear Functions and how real world situations can be modeled using Linear Functions. We study the relationship between Average Rate of Change and Slope and how
More informationAlgebra I Calculator Activities
First Nine Weeks SOL Objectives Calculating Measures of Central Tendency SOL A.17 Organize a set of data Calculate the mean, median, mode, and range of a set of data Describe the relationships between
More informationH.Algebra 2 Summer Review Packet
H.Algebra Summer Review Packet 1 Correlation of Algebra Summer Packet with Algebra 1 Objectives A. Simplifing Polnomial Epressions Objectives: The student will be able to: Use the commutative, associative,
More informationPure Math 30: Explained!
Pure Math 30: Eplained! www.puremath30.com 9 Logarithms Lesson PART I: Eponential Functions Eponential functions: These are functions where the variable is an eponent. The first type of eponential graph
More informationSAT RELEASED TEST ADMINISTERED ON APRIL 10, 2018 CLASSROOM SAT SESSION #6
SAT RELEASED TEST ADMINISTERED ON APRIL 10, 2018 CLASSROOM SAT SESSION #6 Calculator Portion Released Test: 18.) The velocity v, in meters per second, of a falling object on Earth after t seconds, ignoring
More informationUsing Tables and Graphing Calculators in Math 11
Using Tables and Graphing Calculators in Math 11 Graphing calculators are not required for Math 11, but they are likely to be helpful, primarily because they allow you to avoid the use of tables in some
More informationStatistical Calculations and Tests Using the TI 83/84.
Statistical Calculations and Tests Using the TI 83/84. The document is meant to be read with a calculator in hand. Work an example to see the results of every step. The content is in the order that the
More informationRegression Using an Excel Spreadsheet Using Technology to Determine Regression
Regression Using an Excel Spreadsheet Enter your data in columns A and B for the x and y variable respectively Highlight the entire data series by selecting it with the mouse From the Insert menu select
More informationThe American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet
The American School of Marrakesh Algebra Algebra Summer Preparation Packet Summer 016 Algebra Summer Preparation Packet This summer packet contains eciting math problems designed to ensure our readiness
More informationInferential Statistics and Distributions
13 Inferential Statistics and Distributions Contents Getting Started: Mean Height of a Population... 13-2 Inferential Stat Editors... 13-6 STAT TESTS Menu... 13-9 Inferential Statistics Input Descriptions...
More informationAlgebra II Notes Quadratic Functions Unit Applying Quadratic Functions. Math Background
Applying Quadratic Functions Math Background Previously, you Graphed and solved quadratic functions. Solved literal equations for a given variable. Found the inverse for a linear function. Verified by
More informationCan you tell the relationship between students SAT scores and their college grades?
Correlation One Challenge Can you tell the relationship between students SAT scores and their college grades? A: The higher SAT scores are, the better GPA may be. B: The higher SAT scores are, the lower
More informationChapter 9. Correlation and Regression
Chapter 9 Correlation and Regression Lesson 9-1/9-2, Part 1 Correlation Registered Florida Pleasure Crafts and Watercraft Related Manatee Deaths 100 80 60 40 20 0 1991 1993 1995 1997 1999 Year Boats in
More informationRegressions of Olympic Proportions
About the Lesson In this activity, students use the Manual-Fit and Linear Regression commands to find lines of best fit to model data from the Olympic Games. As a result, students will: Develop and evaluate
More informationINTRODUCTION GOOD LUCK!
INTRODUCTION The Summer Skills Assignment for has been developed to provide all learners of our St. Mar s Count Public Schools communit an opportunit to shore up their prerequisite mathematical skills
More informationMathematical Modeling
Mathematical Modeling Sample Problem: The chart below gives the profit for a company for the years 1990 to 1999, where 0 corresponds to 1990 and the profit is in millions of dollars. Year 0 1 2 3 4 5 6
More informationChapter 11. Correlation and Regression
Chapter 11 Correlation and Regression Correlation A relationship between two variables. The data can be represented b ordered pairs (, ) is the independent (or eplanator) variable is the dependent (or
More informationS12 - HS Regression Labs Workshop. Linear. Quadratic (not required) Logarithmic. Exponential. Power
Summer 2006 I2T2 Probability & Statistics Page 181 S12 - HS Regression Labs Workshop Regression Types: Needed for Math B Linear Quadratic (not required) Logarithmic Exponential Power You can calculate
More information6.1.1 How can I make predictions?
CCA Ch 6: Modeling Two-Variable Data Name: Team: 6.1.1 How can I make predictions? Line of Best Fit 6-1. a. Length of tube: Diameter of tube: Distance from the wall (in) Width of field of view (in) b.
More informationBIVARIATE DATA data for two variables
(Chapter 3) BIVARIATE DATA data for two variables INVESTIGATING RELATIONSHIPS We have compared the distributions of the same variable for several groups, using double boxplots and back-to-back stemplots.
More informationReteach 2-3. Graphing Linear Functions. 22 Holt Algebra 2. Name Date Class
-3 Graphing Linear Functions Use intercepts to sketch the graph of the function 3x 6y 1. The x-intercept is where the graph crosses the x-axis. To find the x-intercept, set y 0 and solve for x. 3x 6y 1
More information3.2 Quadratic Equations by Graphing
www.ck12.org Chapter 3. Quadratic Equations and Quadratic Functions 3.2 Quadratic Equations by Graphing Learning Objectives Identify the number of solutions of quadratic equations. Solve quadratic equations
More informationChapter 10 Regression Analysis
Chapter 10 Regression Analysis Goal: To become familiar with how to use Excel 2007/2010 for Correlation and Regression. Instructions: You will be using CORREL, FORECAST and Regression. CORREL and FORECAST
More informationObjectives. Materials
. Objectives Activity 6 To investigate the relationship between mass and volume To find the x value of a function, given the y value To find the y value of a function, given the x value To use technology
More informationLesson 3 Average Rate of Change and Linear Functions
Lesson 3 Average Rate of Change and Linear Functions Lesson 3 Average Rate of Change and Linear Functions In this lesson, we will introduce the concept of average rate of change followed by a review of
More informationOHS Algebra 2 Summer Packet
OHS Algebra 2 Summer Packet Good Luck to: Date Started: (please print student name here) Geometry Teacher s Name: Complete each of the following exercises in this formative assessment. To receive full
More informationChill Out: How Hot Objects Cool
Chill Out: How Hot Objects Cool Activity 17 When you have a hot drink, you know that it gradually cools off. Newton s law of cooling provides us with a model for cooling. It states that the temperature
More informationAccel Alg E. L. E. Notes Solving Quadratic Equations. Warm-up
Accel Alg E. L. E. Notes Solving Quadratic Equations Warm-up Solve for x. Factor. 1. 12x 36 = 0 2. x 2 8x Factor. Factor. 3. 2x 2 + 5x 7 4. x 2 121 Solving Quadratic Equations Methods: (1. By Inspection)
More information2. LECTURE 2. Objectives
2. LECTURE 2 Objectives I understand the distinction between independent variable(s) and the corresponding dependent variable as well as why that distinction was chosen for the situation. I can define
More informationBARUCH COLLEGE MATH 2207 FALL 2007 MANUAL FOR THE UNIFORM FINAL EXAMINATION. No calculator will be allowed on this part.
BARUCH COLLEGE MATH 07 FALL 007 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final eamination for Math 07 will consist of two parts. Part I: Part II: This part will consist of 5 questions. No calculator
More informationMPM2D - Practice Mastery Test #5
MPM2D - Practice Mastery Test #5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2. If, then x = a. -4 b. -3 c. 1 d. 2 3. Simplify 4. Select the table
More informationAlgebra Review. Finding Zeros (Roots) of Quadratics, Cubics, and Quartics. Kasten, Algebra 2. Algebra Review
Kasten, Algebra 2 Finding Zeros (Roots) of Quadratics, Cubics, and Quartics A zero of a polynomial equation is the value of the independent variable (typically x) that, when plugged-in to the equation,
More informationHistorical Note. Regression. Line of Best Fit
11 4 Regression Objective 4. Compute the equation of the regression line. In studing relationships between two variables, collect the data and then construct a scatter plot. The purpose of the scatter
More informationPolynomial Functions and Their Graphs. Definition of a Polynomial Function: numbers, with a n 0. The function defined by
Polynomial Functions and Their Graphs Definition of a Polynomial Function: Let n be a nonnegative number and let a n, a n 1, a 2, a 1, a 0 be real numbers, with a n 0. The function defined by f(x) = a
More informationNUMB3RS Activity: How Does it Fit?
Name Regression 1 NUMB3RS Activity: How Does it Fit? A series of sniper shootings has reduced the city of Los Angeles to a virtual ghost town. To help solve the shootings, the FBI has enlisted the help
More informationContents 16. Higher Degree Equations
Contents 16. Higher Degree Equations 2 16.3 Finding Roots of Higher Degree Equations................. 2 Example 16.15............................... 2 Example 16.16............................... 2 Example
More informationFoundations for Functions
Activity: TEKS: Overview: Materials: Regression Exploration (A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (D) collect and organize
More informationMA 1128: Lecture 08 03/02/2018. Linear Equations from Graphs And Linear Inequalities
MA 1128: Lecture 08 03/02/2018 Linear Equations from Graphs And Linear Inequalities Linear Equations from Graphs Given a line, we would like to be able to come up with an equation for it. I ll go over
More informationSteps to take to do the descriptive part of regression analysis:
STA 2023 Simple Linear Regression: Least Squares Model Steps to take to do the descriptive part of regression analysis: A. Plot the data on a scatter plot. Describe patterns: 1. Is there a strong, moderate,
More information2015 SUMMER MATH PACKET
Name: Date: 05 SUMMER MATH PACKET College Algebra Trig. - I understand that the purpose of the summer packet is for my child to review the topics they have already mastered in previous math classes and
More informationHeinemann VCE Zone textbook reference General Mathematics
Contents Cross-reference table for TI-Nspire CAS skills required for Heinemann VCE Zone: General, Heinemann VCE Zone: Further and Heinemann VCE Zone: Specialist. Code Description TS.1 Rounding off 4 TS.2
More informationBivariate Data Summary
Bivariate Data Summary Bivariate data data that examines the relationship between two variables What individuals to the data describe? What are the variables and how are they measured Are the variables
More information1.2 Supplement: Mathematical Models: A Catalog of Essential Functions
Math 131 -copyright Angela Allen, Fall 2011 1 1.2 Supplement: Mathematical Models: A Catalog of Essential Functions Note: Some of these examples and figures come from your textbook Single Variable Calculus:
More informations e, which is large when errors are large and small Linear regression model
Linear regression model we assume that two quantitative variables, x and y, are linearly related; that is, the the entire population of (x, y) pairs are related by an ideal population regression line y
More informationComplete Week 8 Package
Complete Week 8 Package Algebra1Teachers @ 2015 Table of Contents Unit 3 Pacing Chart -------------------------------------------------------------------------------------------- 1 Lesson Plans --------------------------------------------------------------------------------------------
More informationProb/Stats Questions? /32
Prob/Stats 10.4 Questions? 1 /32 Prob/Stats 10.4 Homework Apply p551 Ex 10-4 p 551 7, 8, 9, 10, 12, 13, 28 2 /32 Prob/Stats 10.4 Objective Compute the equation of the least squares 3 /32 Regression A scatter
More informationCorrelation and Regression (Excel 2007)
Correlation and Regression (Excel 2007) (See Also Scatterplots, Regression Lines, and Time Series Charts With Excel 2007 for instructions on making a scatterplot of the data and an alternate method of
More informationName Class Date. Residuals and Linear Regression Going Deeper
Name Class Date 4-8 and Linear Regression Going Deeper Essential question: How can you use residuals and linear regression to fit a line to data? You can evaluate a linear model s goodness of fit using
More informationChapter 1 Functions and Models
Chapter 1 Functions and Models 1.2 Mathematical Models: A catalog of Essential Functions A mathematical model is a mathematical description of a real world situations such as the size of a population,
More informationInference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
More informationName. The data below are airfares to various cities from Baltimore, MD (including the descriptive statistics).
Name The data below are airfares to various cities from Baltimore, MD (including the descriptive statistics). 178 138 94 278 158 258 198 188 98 179 138 98 N Mean Std. Dev. Min Q 1 Median Q 3 Max 12 166.92
More informationStoichiometry a Functional Point of View Pedagogy (Math/Science Connection)
Stoichiometry a Functional Point of View Pedagogy (Math/Science Connection) Stoichiometry problems are often solved by using dimensional analysis. Dimensional analysis is a very useful tool and was probably
More informationUnit 2, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 2 - Polynomial Equations & Inequalities 2.1 Laws of Exponents - record the rules for
More informationLAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION
LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION In this lab you will learn how to use Excel to display the relationship between two quantitative variables, measure the strength and direction of the
More informationReview 6. n 1 = 85 n 2 = 75 x 1 = x 2 = s 1 = 38.7 s 2 = 39.2
Review 6 Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected ) A researcher finds that of,000 people who said that
More informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationLecture 46 Section Tue, Apr 15, 2008
ar Koer ar Lecture 46 Section 13.3.2 Koer Hampden-Sydney College Tue, Apr 15, 2008 Outline ar Koer 1 2 3 4 5 ar Koer We are now ready to calculate least-squares regression line. formulas are a bit daunting,
More informationChapter 6 Logarithmic and Exponential Functions
Chapter 6 Logarithmic and Eponential Functions 6.1 The Definition of e Eample 1 Consider the eponential function f 1 ( ) 1 What happens to f() as gets very large? Type the function into Y=. Let Y 1 1 1/.
More information3 9 Curve Fitting with Polynomials
3 9 Curve Fitting with Polynomials Relax! You will do fine today! We will review for quiz!!! (which is worth 10 points, has 20 questions, group, graphing calculator allowed, and will not be on your first
More informationSections 6.1 and 6.2: Systems of Linear Equations
What is a linear equation? Sections 6.1 and 6.2: Systems of Linear Equations We are now going to discuss solving systems of two or more linear equations with two variables. Recall that solving an equation
More informationMath 12 - for 4 th year math students
Math 12 - for 4 th year math students This portion of the entire unit should be completed in 6 days The students will utilize handout notes, measuring tapes, textbooks, and graphing calculators for all
More informationAP Statistics Two-Variable Data Analysis
AP Statistics Two-Variable Data Analysis Key Ideas Scatterplots Lines of Best Fit The Correlation Coefficient Least Squares Regression Line Coefficient of Determination Residuals Outliers and Influential
More informationDescribing Bivariate Relationships
Describing Bivariate Relationships Bivariate Relationships What is Bivariate data? When exploring/describing a bivariate (x,y) relationship: Determine the Explanatory and Response variables Plot the data
More informationAP Physics 1 Summer Packet
AP Physics 1 Summer Packet Dear future AP Physics 1 Student: Welcome to the wonderful world of physics. In an effort to make the most of our limited time together next year is it essential that you come
More informationUnit Calendar. Date Sect. Topic Homework HW On-Time Apr , 2, 3 Quadratic Equations & Page 638: 3-11 Page 647: 3-29, odd
Name/Period: Unit Calendar Date Sect. Topic Homework HW On-Time Apr. 4 10.1, 2, 3 Quadratic Equations & Page 638: 3-11 Graphs Page 647: 3-29, odd Apr. 6 9.4 10.4 Solving Quadratic Equations by Factoring
More informationClassroom Assessments Based on Standards Integrated College Prep I Unit 3 CP 103A
Classroom Assessments Based on Standards Integrated College Prep I Unit 3 CP 103A Name: ID Number: Teacher Name: Score: Proficient: yes no How Tall Can He Be? The table below shows the average height in
More informationAlgebra II: Strand 2. Linear Functions; Topic 2. Slope and Rate of Change; Task 2.2.1
1 TASK 2.2.1: AVERAGE RATES OF CHANGE Solutions One of the ways in which we describe functions is by whether they are increasing, decreasing, or constant on an interval in their domain. If the graph of
More informationChapter 4: Regression Models
Sales volume of company 1 Textbook: pp. 129-164 Chapter 4: Regression Models Money spent on advertising 2 Learning Objectives After completing this chapter, students will be able to: Identify variables,
More informationSUMMER MATH PACKET College Algebra and Trigonometry A COURSE 235 and Pre-Calculus A COURSE 241
SUMMER MATH PACKET College Algebra and Trigonometry A COURSE 35 and Pre-Calculus A COURSE 41 Revised May 017 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for
More informationCorrelation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down)
Two-Variable Statistics Correlation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down) Positive Correlation As one variable
More informationy = a + bx 12.1: Inference for Linear Regression Review: General Form of Linear Regression Equation Review: Interpreting Computer Regression Output
12.1: Inference for Linear Regression Review: General Form of Linear Regression Equation y = a + bx y = dependent variable a = intercept b = slope x = independent variable Section 12.1 Inference for Linear
More informationAMS 7 Correlation and Regression Lecture 8
AMS 7 Correlation and Regression Lecture 8 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Suumer 2014 1 / 18 Correlation pairs of continuous observations. Correlation
More informationScatterplots. 3.1: Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Section 3.1 Scatterplots and Correlation
3.1: Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal
More informationObjectives Simple linear regression. Statistical model for linear regression. Estimating the regression parameters
Objectives 10.1 Simple linear regression Statistical model for linear regression Estimating the regression parameters Confidence interval for regression parameters Significance test for the slope Confidence
More informationM&M Exponentials Exponential Function
M&M Exponentials Exponential Function Teacher Guide Activity Overview In M&M Exponentials students will experiment with growth and decay functions. Students will also graph their experimental data and
More informationIntroduction to Limits
MATH 136 Introduction to Limits Given a function y = f (x), we wish to describe the behavior of the function as the variable x approaches a particular value a. We should be as specific as possible in describing
More informationBusiness Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
More information5.1 Bivariate Relationships
Chapter 5 Summarizing Bivariate Data Source: TPS 5.1 Bivariate Relationships What is Bivariate data? When exploring/describing a bivariate (x,y) relationship: Determine the Explanatory and Response variables
More informationThe Chi-Square Distributions
MATH 03 The Chi-Square Distributions Dr. Neal, Spring 009 The chi-square distributions can be used in statistics to analyze the standard deviation of a normally distributed measurement and to test the
More informationLeast-Squares Regression
MATH 203 Least-Squares Regression Dr. Neal, Spring 2009 As well as finding the correlation of paired data {{ x 1, y 1 }, { x 2, y 2 },..., { x n, y n }}, we also can plot the data with a scatterplot and
More informationTalking feet: Scatterplots and lines of best fit
Talking feet: Scatterplots and lines of best fit Student worksheet What does your foot say about your height? Can you predict people s height by how long their feet are? If a Grade 10 student s foot is
More informationMiddle grade students are the intended audience; however, portions of the lesson may be
. Traveling Through the Solar System Introduction Traveling Through the Solar System NCTM Standards Approximate time needed for lesson: Two 50-minute class periods or one 90-minute class period Measurement:
More information3.7 Linear and Quadratic Models
3.7. Linear and Quadratic Models www.ck12.org 3.7 Linear and Quadratic Models Learning Objectives Identif functions using differences and ratios. Write equations for functions. Perform eponential and quadratic
More informationChapter 14 Simple Linear Regression (A)
Chapter 14 Simple Linear Regression (A) 1. Characteristics Managerial decisions often are based on the relationship between two or more variables. can be used to develop an equation showing how the variables
More information3.1 Notes for Lines and Linear Growth: What does a constant rate mean?
3.1 Notes for Lines and Linear Growth: What does a constant rate mean? Key concept: A function is called _Linear_ if it has a _Constant growth rate You take notes and put in your own words. What is positive
More informationLet the x-axis have the following intervals:
1 & 2. For the following sets of data calculate the mean and standard deviation. Then graph the data as a frequency histogram on the corresponding set of axes. Set 1: Length of bass caught in Conesus Lake
More informationSTAT Chapter 11: Regression
STAT 515 -- Chapter 11: Regression Mostly we have studied the behavior of a single random variable. Often, however, we gather data on two random variables. We wish to determine: Is there a relationship
More informationThe Chi-Square Distributions
MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation σ of a normally distributed measurement and to test the goodness
More information