Chapter 23. Inferences for Regression


 Arnold Fletcher
 2 years ago
 Views:
Transcription
1 Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants four to ten days old and their later IQ test scores. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. They later measured the children s IQ at age three years using the Stanford Binet IQ test. Do children with higher crying counts tend to have higher IQ? 1. Create a scatterplot: a. Open data set ta2301.por. b. Click Graphs, scroll to Legacy Dialogs then Scatter/Dot. c. Click on Simple Scatter, then click on Define. d. Move IQ into the Y Axis box since IQ is the response variable e. Move Crycount into the X Axis box since Crycount is the explanatory variable. 149
2 f. Click OK. The scatterplot will appear in the output window. Inferences for Regression 150
3 151 Chapter Find the leastsquares regression line. a. Click Analyze. Scroll to Regression then Linear. b. Move IQ to the Dependent box. c. Move Crycount to the Independent box. d. Click OK.
4 Inferences for Regression 152 The least squares regression line is given by yˆ = x. The slope of the least squares regression line, 1.493, is found in the Coefficients table under the B column in the row for Crycount. The yintercept of the least squares regression line, , is also found in the Coefficients table under the B column in the Constant row. Example 23.7: Beer and blood alcohol The Problem: The EESEE story Blood Alcohol Content describes a study in which 16 student volunteers at the Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don t believe that number of drinks predicts blood alcohol well. Steven thinks he can drive legally 30 minutes after he finishes 5 beers. The legal limit for driving is BAC 0.08 in all states. We want to predict Steve s blood alcohol content, using no information except that he drinks 5 beers. 1. Regress BAC on number of beers. a. Open the data set eg2307.por. b. Click Analyze, scroll down to Regression, then click Linear. c. Move BAC to the Dependent box. d. Move Beers to the Independent box.
5 153 Chapter Display predicted values and residuals. a. Click the Save button at the right of the window. b. Under Predicted Values select Unstandardized. c. Under Residuals select Unstandardized. d. Click Continue. 3. Create a 95% Confidence Interval. a. Click the Statistics button. b. Under Regression Coefficients select Confidence Intervals.
6 Inferences for Regression 154 c. Click Continue. d. Click OK. A new window will pop up with the output.
7 155 Chapter 23 e. The predicted values and residuals can be seen on the data sheet as 2 new columns PRE_1 and RES_1. Notice that the predicted BAC when a person drinks 5 beers is
8 Inferences for Regression 156 Chapter 23 Exercises 23.1 Ebola and gorillas Great Arctic rivers Great Arctic rivers: testing Ebola and gorillas: testing correlation Ebola and gorillas: estimating slope Great Arctic rivers: estimating slope Manatees: conditions for inference Predicting tropical storms Squirrels and their food supply Beavers and beetles.
9 453 Chapter 23 SPSS Solutions 23.1 Use Graphs, Legacy Dialogs, Scatter/Dot to create a plot of the data. The plot is strongly linear and increasing. We could use Analyze, Correlate, Bivariate to find the correlation, but we also want to find the regression equation, so use Analyze, Regression to compute the regression equation (we ll use the square root of r 2 as the correlation). We can have SPSS find the residuals for us by clicking Save and checking the box for Unstandardized residuals.
10 454 Model R R Square Model Summary b Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Distance b. Dependent Variable: Days Coefficients a Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Distance a. Dependent Variable: Days The correlation is r = a very strong relationship. Our estimated slope of b = says the virus takes about days for each additional home range it must travel. The estimated intercept is a = The standard deviation around the regression line is s = (labeled as Std. Error of the Estimate). To sum (or find the mean of) the residuals (created as variable RES_1) use Analyze, Descriptive Statistics, Descriptives. With a mean of , the sum must be 0. Descriptive Statistics N Minimum Maximum Mean Std. Deviation Unstandardized Residual Valid N (listwise) 6
11 We define a scatterplot of the data in ta To add the regression line in the graph, doubleclick for the Chart Editor, then click Elements, Fit line at total. There is an increasing trend in the graph, with lots of scatter. SPSS gives r 2 = 0.112; the relationship is fairly weak. Only 11% of the variation in discharge is explained by time (year); there certainly are other factors involved. Use Analyze, Regression, Linear to fit the regression. Looking ahead, we have asked for confidence intervals for the coefficients using the Statistics button. Unstandardized Coefficients Coefficients a Standardized Coefficients Model B Std. Error Beta t Sig. 1 95% Confidence Interval for B Lower Bound Upper Bound (Constant) Year a. Dependent Variable:
12 456 Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), The regression equation is Discharge = *Year. The regression standard error is s = From the SPSS output in Exericise 23.3, the test statistic is t = with (twosided) Pvalue The onesided Pvalue is Since this Pvalue is less than any standard α, we reject a null hypothesis of no relationship and conclude that these data do show an increase in Arctic river discharge (supporting the global warming hypothesis) Refer to the solution for Exercise 23.1 In the SPSS results, we were given t = 7.08 and P = Since this is a twosided Pvalue, divide by 2. The onesided Pvalue is Minitab gives the same (twosided) Pvalue for the correlation if you use Stat, Basic Statistics, Correlation. If we use Analyze, Correlate, Bivariate, and ask for the onesided Pvalue, we have the same result. Correlations Distance Days Distance Days Pearson Correlation ** Sig. (1tailed).001 N Pearson Correlation.962 ** Sig. (1tailed).001 N **. Correlation is significant at the 0.01 level (1tailed).
13 SPSS will find the 95% confidence interval if you redo the regression and click Statistics, then check the box to ask for confidence intervals for the coefficients. Unstandardized Coefficients Coefficients a Standardized Coefficients Model B Std. Error Beta t Sig. 1 95% Confidence Interval for B Lower Bound Upper Bound (Constant) Distance a. Dependent Variable: Days We have the same output as in Exercise 23.1, with the addition of confidence bounds at the right side. Based on this data, Ebola takes between 6.85 and days to travel one home range, with 95% confidence. However, the problem asked for 90% confidence. For this, we use Transform, Compute Variable to find t*, then compute the interval by hand. The interval is ± 2.132*1.591 = (7.871, ). Based on this data, Ebola takes between 7.87 and days to travel one home range, with 90% confidence SPSS gives only 95% confidence intervals for regression parameters. We saw in Exercise 23.3 that a 95% confidence interval for the slope is from to
14 458 However, this question asks for a 90% confidence interval. We use Transform, Compute Variable to find t* (degrees of freedom are n 2), then compute the interval by hand. The confidence interval is calculated as b± t* SE( b), giving ±1.670*0.7037, or (0.791, 3.141). We are 90% confident that arctic river discharge increases between and cubic kilometers per year. Since the low end is positive, we re convinced that discharge is increasing over time To make the stemplot, use Analyze, Descriptive Statistics, Explore. StemandLeaf Plot Frequency Stem & Leaf Stem width: Each leaf: 1 case(s) This plot is pretty symmetric and bellshaped with no outliers. The Normal assumption is reasonable for these residuals. To make the scatterplot, use Graphs, Legacy Dialogs, Scatter/Dot. Use Residual on the y axis and Boats on the x axis. To add the residual = 0 line, double click in the graph for the Chart Editor, then click Options, Y axis reference line. Close the properties window and the Chart editor. The plot is random (no discernable pattern), so the regression model is reasonable. While pollution may have caused some manatee deaths, the data are labeled as manatees killed by boats, so pollution would not explain more of these deaths.
15 23.33 We create a scatterplot of Dr. Gray s predictions against actual storms and compute the regression. 459
16 460 There is a positive relationship seen in the graph; however, there are a couple of years in which he predicted a large number of storms and the actual number was much less. Part (b) asks for a 95% confidence interval for the mean number of storms when Dr. Gray predicts 16 storms. To do this, add a forecast value of 16 in the spreadsheet (SPSS will only create prediction and confidence intervals for values in the spreadsheet), then in the Analyze, Regression, Linear dialog box, click Save and check the box for Mean Prediction Intervals. Model R R Square Model Summary b Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), b. Dependent Variable: Model 1 Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta (Constant) t Sig. Forecast a. Dependent Variable: The regression equation is ActualStorms = *Predicted. With a t statistic of and (twosided) Pvalue of (so, the onesided Pvalue is 0.004), the relationship is significantly positive. Return to the data spreadsheet. SPSS has created 95% confidence intervals for each value of Forecast. At the bottom, we see the values for the interval of interest.
17 461 We predict the mean number of actual storms for years when Professor Gray predicts 16 will be between and 19.73, with 95% confidence. If you wanted values for a particular year, you would have checked the box for Individual Prediction Intervals in the Save dialog box We create a scatterplot of the Cones as the X axis variable and Offspring as the Y axis variable using Graphs, Legacy Dialogs, Scatter/Dot. The pattern is roughly linear (there is a fair amount of scatter) and increasing more cones seem to be associated with more offspring.
18 462 Use Analyze, Regression, Linear to find linear regression and measures of association. We will want to examine the residuals for adequacy of the regression, so click Save and check the box for Unstandardized Residuals. You can also ask for a histogram of the standardized residuals these are zscores (and a Normal plot of them) in the Plots box. The regression equation is Offspring = *Cones. The relationship is fairly strong r = 0.756; the cone index explains r 2 = 57.2% of the variation in offspring. Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Cones Coefficients a Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Cones a. Dependent Variable: Offspring The relationship is indeed statistically significant; we have t = with (twosided) P = 0.001, so the onesided Pvalue is
19 There are some gaps in the histogram, but with the imposed density curve, the Normal assumption seems reasonable. Note the mean of these is (essentially) 0. Create a scatterplot of the saved residuals against the cone index using Graphs, Legacy Dialogs, Scatter/Dot. This plot shows no definite pattern, so our inference is reliable. 463
20 Open data file ex First, create a scatterplot of the data using Graphs, Legacy Dialogs, Scatter/Dot. Enter Stumps as the X variable and Larvae as the Y variable. Give your graph an appropriate title using Titles. We see that these data indicate that there are more beetle larvae with more stumps. Use Analyze, Regression, Linear to fit the line using Stumps as the Independent and Larvae as the Dependent. We d like a 95% confidence interval for the slope (how many more clusters accompany each additional stump), so click Statistics, and check the box for Confidence Intervals. Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Stumps Unstandardized Coefficients Coefficients a Standardized Coefficients Model B Std. Error Beta t Sig. 1 95% Confidence Interval for B Lower Bound Upper Bound (Constant) Stumps a. Dependent Variable:
21 465 The regression equation is Larvae = * Stumps. The relationship is strong; the regression model explains 84.3% of the variability in larvae (the correlation is r = r =.843 =0.918). We are confident that more stumps lead to more larvae because the 95% confidence for the slope is between 9.53 and which is well above 0. Our scatterplot of the residuals against Stumps (the predictor variable) indicates no discernable pattern, so this regression model is reasonable.
Simple Linear Regression in SPSS STAT 314
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,
More informationChapter 5. Regression
Topics covered in this chapter: Chapter 5. Regression Adding a Regression Line to a Scatterplot Regression Lines and Influential Observations Finding the Least Squares Regression Model Adding a Regression
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationSimple Linear Regression, Scatterplots, and Bivariate Correlation
1 Simple Linear Regression, Scatterplots, and Bivariate Correlation This section covers procedures for testing the association between two continuous variables using the SPSS Regression and Correlate analyses.
More informationLinear Regression in SPSS
Linear Regression in SPSS Data: mangunkill.sav Goals: Examine relation between number of handguns registered (nhandgun) and number of man killed (mankill) checking Predict number of man killed using number
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a stepbystep guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationOnce saved, if the file was zipped you will need to unzip it.
1 Commands in SPSS 1.1 Dowloading data from the web The data I post on my webpage will be either in a zipped directory containing a few files or just in one file containing data. Please learn how to unzip
More informationA Guide for a Selection of SPSS Functions
A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University  2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer
More informationExample: Boats and Manatees
Figure 96 Example: Boats and Manatees Slide 1 Given the sample data in Table 91, find the value of the linear correlation coefficient r, then refer to Table A6 to determine whether there is a significant
More informationDoing Multiple Regression with SPSS. In this case, we are interested in the Analyze options so we choose that menu. If gives us a number of choices:
Doing Multiple Regression with SPSS Multiple Regression for Data Already in Data Editor Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options:
More informationSummarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationAn SPSS companion book. Basic Practice of Statistics
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationUsing Minitab for Regression Analysis: An extended example
Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More information2. Simple Linear Regression
Research methods  II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationFormula for linear models. Prediction, extrapolation, significance test against zero slope.
Formula for linear models. Prediction, extrapolation, significance test against zero slope. Last time, we looked the linear regression formula. It s the line that fits the data best. The Pearson correlation
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationSPSS TUTORIAL & EXERCISE BOOK
UNIVERSITY OF MISKOLC Faculty of Economics Institute of Business Information and Methods Department of Business Statistics and Economic Forecasting PETRA PETROVICS SPSS TUTORIAL & EXERCISE BOOK FOR BUSINESS
More informationTable of Contents. Preface
Table of Contents Preface Chapter 1: Introduction 11 Opening an SPSS Data File... 2 12 Viewing the SPSS Screens... 3 o Data View o Variable View o Output View 13 Reading NonSPSS Files... 6 o Convert
More informationSPSS: Descriptive and Inferential Statistics. For Windows
For Windows August 2012 Table of Contents Section 1: Summarizing Data...3 1.1 Descriptive Statistics...3 Section 2: Inferential Statistics... 10 2.1 ChiSquare Test... 10 2.2 T tests... 11 2.3 Correlation...
More informationKSTAT MINIMANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINIMANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
More informationBill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1
Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationDirections for using SPSS
Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...
More informationCorrelation and Regression
Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look
More informationChapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
More informationRegression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between
More informationBivariate Analysis. Correlation. Correlation. Pearson's Correlation Coefficient. Variable 1. Variable 2
Bivariate Analysis Variable 2 LEVELS >2 LEVELS COTIUOUS Correlation Used when you measure two continuous variables. Variable 2 2 LEVELS X 2 >2 LEVELS X 2 COTIUOUS ttest X 2 X 2 AOVA (Ftest) ttest AOVA
More informationThe ChiSquare Test. STAT E50 Introduction to Statistics
STAT 50 Introduction to Statistics The ChiSquare Test The Chisquare test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed
More informationData analysis and regression in Stata
Data analysis and regression in Stata This handout shows how the weekly beer sales series might be analyzed with Stata (the software package now used for teaching stats at Kellogg), for purposes of comparing
More informatione = random error, assumed to be normally distributed with mean 0 and standard deviation σ
1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.
More informationStat 412/512 CASE INFLUENCE STATISTICS. Charlotte Wickham. stat512.cwick.co.nz. Feb 2 2015
Stat 412/512 CASE INFLUENCE STATISTICS Feb 2 2015 Charlotte Wickham stat512.cwick.co.nz Regression in your field See website. You may complete this assignment in pairs. Find a journal article in your field
More informationFor example, enter the following data in three COLUMNS in a new View window.
Statistics with Statview  18 Paired ttest A paired ttest compares two groups of measurements when the data in the two groups are in some way paired between the groups (e.g., before and after on the
More information, has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.
BA 275 Review Problems  Week 9 (11/20/0611/24/06) CD Lessons: 69, 70, 1620 Textbook: pp. 520528, 111124, 133141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An
More informationCorrelation and Regression Analysis: SPSS
Correlation and Regression Analysis: SPSS Bivariate Analysis: Cyberloafing Predicted from Personality and Age These days many employees, during work hours, spend time on the Internet doing personal things,
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationJanuary 26, 2009 The Faculty Center for Teaching and Learning
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationScatter Plot, Correlation, and Regression on the TI83/84
Scatter Plot, Correlation, and Regression on the TI83/84 Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. This page
More informationStatistics 151 Practice Midterm 1 Mike Kowalski
Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and
More informationStatistical Analysis Using SPSS for Windows Getting Started (Ver. 2014/11/6) The numbers of figures in the SPSS_screenshot.pptx are shown in red.
Statistical Analysis Using SPSS for Windows Getting Started (Ver. 2014/11/6) The numbers of figures in the SPSS_screenshot.pptx are shown in red. 1. How to display English messages from IBM SPSS Statistics
More information2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or
Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.$ and Sales $: 1. Prepare a scatter plot of these data. The scatter plots for Adv.$ versus Sales, and Month versus
More informationAn analysis appropriate for a quantitative outcome and a single quantitative explanatory. 9.1 The model behind linear regression
Chapter 9 Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative explanatory variable. 9.1 The model behind linear regression When we are examining the relationship
More informationThere are six different windows that can be opened when using SPSS. The following will give a description of each of them.
SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet
More informationMultiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear. In the main dialog box, input the dependent variable and several predictors.
More informationGeoGebra Statistics and Probability
GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,
More informationSPSS Explore procedure
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stemandleaf plots and extensive descriptive statistics. To run the Explore procedure,
More informationAn analysis method for a quantitative outcome and two categorical explanatory variables.
Chapter 11 TwoWay ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that
More informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationData Analysis. Using Excel. Jeffrey L. Rummel. BBA Seminar. Data in Excel. Excel Calculations of Descriptive Statistics. Single Variable Graphs
Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships
More informationSPSS BASICS. (Data used in this tutorial: General Social Survey 2000 and 2002) Ex: Mother s Education to eliminate responses 97,98, 99;
SPSS BASICS (Data used in this tutorial: General Social Survey 2000 and 2002) How to do Recoding Eliminating Response Categories Ex: Mother s Education to eliminate responses 97,98, 99; When we run a frequency
More informationRegression stepbystep using Microsoft Excel
Step 1: Regression stepbystep using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression
More informationBivariate Regression Analysis. The beginning of many types of regression
Bivariate Regression Analysis The beginning of many types of regression TOPICS Beyond Correlation Forecasting Two points to estimate the slope Meeting the BLUE criterion The OLS method Purpose of Regression
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More informationEXCEL Tutorial: How to use EXCEL for Graphs and Calculations.
EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your
More information11. Analysis of Casecontrol Studies Logistic Regression
Research methods II 113 11. Analysis of Casecontrol Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationBelow is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.
Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data
More informationMultiple Regression. Page 24
Multiple Regression Multiple regression is an extension of simple (bivariate) regression. The goal of multiple regression is to enable a researcher to assess the relationship between a dependent (predicted)
More informationThe Dummy s Guide to Data Analysis Using SPSS
The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationDEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,
More informationCopyright 2013 by Laura Schultz. All rights reserved. Page 1 of 7
Using Your TI83/84/89 Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationABSORBENCY OF PAPER TOWELS
ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?
More informationLesson Lesson Outline Outline
Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and
More informationSTAT 350 Practice Final Exam Solution (Spring 2015)
PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects
More informationUSING A TI83 OR TI84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS
USING A TI83 OR TI84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS W. SCOTT STREET, IV DEPARTMENT OF STATISTICAL SCIENCES & OPERATIONS RESEARCH VIRGINIA COMMONWEALTH UNIVERSITY Table
More informationCopyright 2013 by Laura Schultz. All rights reserved. Page 1 of 6
Using Your TINSpire Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.
More informationAP Statistics 2001 Solutions and Scoring Guidelines
AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More informationMathematics. Probability and Statistics Curriculum Guide. Revised 2010
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More informationMAT 12O ELEMENTARY STATISTICS I
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 12O ELEMENTARY STATISTICS I 3 Lecture Hours, 1 Lab Hour, 3 Credits PreRequisite:
More informationRegression and Correlation
Regression and Correlation Topics Covered: Dependent and independent variables. Scatter diagram. Correlation coefficient. Linear Regression line. by Dr.I.Namestnikova 1 Introduction Regression analysis
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More informationChapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
More informationSPSS Manual for Introductory Applied Statistics: A Variable Approach
SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All
More informationWeek TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480
1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More informationMain Effects and Interactions
Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly
More informationOnce saved, if the file was zipped you will need to unzip it. For the files that I will be posting you need to change the preferences.
1 Commands in JMP and Statcrunch Below are a set of commands in JMP and Statcrunch which facilitate a basic statistical analysis. The first part concerns commands in JMP, the second part is for analysis
More informationUsing Microsoft Excel to Plot and Analyze Kinetic Data
Entering and Formatting Data Using Microsoft Excel to Plot and Analyze Kinetic Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page (Figure 1). Type
More informationDESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS
DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi  110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics
More informationCurve Fitting in Microsoft Excel By William Lee
Curve Fitting in Microsoft Excel By William Lee This document is here to guide you through the steps needed to do curve fitting in Microsoft Excel using the leastsquares method. In mathematical equations
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationSydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.
Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under
More informationForecasting in STATA: Tools and Tricks
Forecasting in STATA: Tools and Tricks Introduction This manual is intended to be a reference guide for time series forecasting in STATA. It will be updated periodically during the semester, and will be
More informationAn introduction to IBM SPSS Statistics
An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More information3: Graphing Data. Objectives
3: Graphing Data Objectives Create histograms, box plots, stemandleaf plots, pie charts, bar graphs, scatterplots, and line graphs Edit graphs using the Chart Editor Use chart templates SPSS has the
More informationLin s Concordance Correlation Coefficient
NSS Statistical Software NSS.com hapter 30 Lin s oncordance orrelation oefficient Introduction This procedure calculates Lin s concordance correlation coefficient ( ) from a set of bivariate data. The
More informationAP Statistics Semester Exam Review Chapters 13
AP Statistics Semester Exam Review Chapters 13 1. Here are the IQ test scores of 10 randomly chosen fifthgrade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you
More informationUsing R for Linear Regression
Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional
More information