1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96


 Frederica Bryant
 1 years ago
 Views:
Transcription
1 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 of operation. To test the validity of this claim, a government testing agency selected a random sample of 100 sets and found that 14 sets required some repair within the first two years of operation. 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = What is the standard error of this confidence interval? ˆp(1 ˆp).14(1.14) SE = = = n What is the margin of error? ME = CV SE = = Set up a 95% confidence interval estimate of the population proportion of TV sets that need repair in the first two years of operation? ( , ) 5. What conclusion can we draw from this confidence interval? Since 0.1 is within the confidence interval, we can conclude that the company s brochure is correct. 6. Interpret the 95% confidence interval. We are 95% confident that the true population proportion is between 8 and 21 percent. 7. What sample size should be taken if the agency wants 95% confidence when the margin of error is 0.05? n = ( CV ME )2 (ˆp(1 ˆp)) = ( )2 (.14(1.14) =
2 2.2 CI 2independent samples Scenario 2 The purchasing director for an industrial factory is investigating the possibility of purchasing a new milling machine. She determines that the new machine will be purchased if there is evidence that the parts produced a higher breaking strength than those from the old machine. The sample standard deviation of the breaking strength for the old machine is 10 kilograms and for the new machine is 9 kilograms. A sample of 25 parts taken from the old machine indicated a sample mean of 65 kilograms, whereas a similar sample of 25 from the new machine indicated a sample mean of 72 kilograms. 1. What are the degrees of freedom? DF = n 1 + n 2 2 = = What is the critical value for this 95% confidence interval? CV = t 0.025,48 = invt (.025, 48) = ± What is the standard error of this confidence interval? Since ME = CV SE, we can solve for SE = ME = 5.41 = CV What is the margin of error? ME = = Set up a 95% confidence interval of the population difference between the two means? (12.41, ) 6. What conclusion can we draw from this confidence interval? Since zero is not within the interval, we can conclude that the new machine has a higher breaking strength than the old machine. The purchasing director should purchase the new machine. 7. Interpret the 95% confidence interval. We are 95% confident that the true mean difference is between and
3 2.3 CI 1 sample T Scenario 3 Suppose an independent testing agency has been contracted to determine whether the contracting company should use a gasoline additive to increase gasoline mileage of its vehicles. The current gasoline mileage for it vehicles is 18.5 mpg. A random sample of 30 vehicles from the company s fleet produced a sample average of mpg and a sample standard deviation of 5.2 mpg. 1. What are the degrees of freedom? DF = n 1 = 30 1 = What is the critical value for this 95% confidence interval? CV = t.025,29 = invt (.025, 29) = ± What is the standard error of this confidence interval? SE = = What is the margin of error? ME = CV SE = = Set up a 95% confidence interval of the population average of the of MPG with gasoline additive? (17.398, ) 6. What conclusion can we draw from this confidence interval? The MPG does not significantly change when the additive was placed in the gasoline. 7. Interpret the 95% confidence interval. We are 95% confident that the true mean is between 17.4 and What sample size should be taken if the agency wants 95% confidence when the margin of error is 1.5? CV SD n = ( ME )2 = ( ) 2 =
4 2.4 CI paired t Scenario 4 Suppose a shoe company wants to test material for the soles of shoes. For each pair of shoes the new material is placed on one shoe and the old material is placed on the other shoe. After a given period of time a random sample of 10 pairs of shoes is selected. The wear is measured on a 10 point scale (higher is better) with the following results. The average of the differences is 0.3 and it standard deviation is What are the degrees of freedom? DF = n 1 = 10 1 = 9 2. What is the critical value for this 95% confidence interval? CV = t.025,9 = invt (.025, 9) = ± What is the standard error of this confidence interval? SE = SD n = = What is the margin of error? ME = CV SE = = Set up a 95% confidence interval of the population difference of paired observations of shoe soles? (0.964, 1.564) 6. What conclusion can we draw from this confidence interval? Since zero is within the confidence interval, we can conclude that there is no difference between the new material and the old material. 7. Interpret the 95% confidence interval. We are 95% confident that the true average difference is between 0.9 and What sample size should be taken if the agency wants 95% confidence when the margin of error is 0.6? CV SD n = ( ME )2 = ( ) 2 =
5 2.5 hypotheses test 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 of operation. To test the validity of this claim, a government testing agency selected a random sample of 100 sets and found that 14 sets required some repair within the first two years of operation. The company uses a 5% level of significance. 1. How many tails have for this test? onetailed which is uppertail 2. What are the hypotheses? H 0 : p 0.1 vs. H 1 : p > What is the standard error of the proportion? p(1 p).1(1.1) SE = = = 0.03 n What is the test statistic? z = What is the pvalue? pvalue = ; do not reject H 0 6. What conclusion can we draw from this test? There is no evidence to reject the company s claim. 7. What is the critical value? z.05 = invnorm(.05) =
6 2.6 hypotheses test 2independent samples Scenario 2 The purchasing director for an industrial factory is investigating the possibility of purchasing a new milling machine. She determines that the new machine will be purchased if there is evidence that the parts produced a higher breaking strength than those from the old machine. The sample standard deviation of the breaking strength for the old machine is 10 kilograms and for the new machine is 9 kilograms. A sample of 25 parts taken from the old machine indicated a sample mean of 65 kilograms, whereas a similar sample of 25 from the new machine indicated a sample mean of 72 kilograms. The director uses a 5% level of significance. 1. How many tails have for this test? one tailed test 2. What are the hypotheses? H 0 : µ o µ n vs. H 1 : µ o < µ n 3. What is the test statistic? t = What are the degrees of freedom? DF = n 1 + n 2 2 = = What is the pvalue? pvalue = Should you reject the null hypothesis (decision)? Yes 7. What conclusion can we draw from this test? There is evidence that the mean breaking strength of the new machine greater than the old machine. 8. What is the critical value? CV = t.05,48 = invt (.05, 48) =
7 2.7 Hypotheses testing 1 sample T Scenario 3 Suppose an independent testing agency has been contracted to determine whether the contracting company should use a gasoline additive. The current gasoline mileage for it vehicles is 18.5 mpg. A random sample of 30 vehicles from the company s fleet produced a sample average of mpg and a sample standard deviation of 5.2 mpg. Is there evidence that putting an additive into the gasoline of the company vehicles will improve the performance (i.e., MPG) of the company vehicles. The company uses a 5% level of significance. 1. How many tails have for this test? upper onetailed test 2. What are the hypotheses? H 0 : µ 18.5 vs. H 1 : µ > What is the test statistic? t = What are the degrees of freedom? DF = n 1 = 30 1 = What is the pvalue? pvalue = Should you reject the null hypothesis (decision)? Do not reject H 0 7. What conclusion can we draw from this test? There is no evidence that the additive actual improved gasoline mileage. 8. What is the critical value? CV = t.05,29 = invt (.95, 29) =
8 2.8 Hypotheses test paired t Scenario 4 Suppose a shoe company wants to test material for the soles of shoes. For each pair of shoes the new material is placed on one shoe and the old material is placed on the other shoe. After a given period of time a random sample of 10 pairs of shoes is selected. The wear is measured on a 10 point scale (higher is better) with the following results. The average of the differences is 0.3 and it standard deviation is Is there evidence the new sole material is different from the current sole material? 1. How many tails have for this test? This is a twotailed test. 2. What are the hypotheses? H 0 : µ d = 0 vs. H 1 : µ d 0 3. What is the test statistic? t = What are the degrees of freedom? DF = n 1 = 10 1 = 9 5. What is the pvalue? pvalue = Should you reject the null hypothesis (decision)? Do not reject H 0 7. What conclusion can we draw from this test? There is no evidence that the new sole material is different from the current sole material. 8. What is the critical value? CV = t.025,9 = invt (.025, 9) = ±
9 2.9 χ 2 test Scenario 5 Suppose the head of the HR division of a midsized company wants to determine if she should let Red Cross have a give blood day in the company cafeteria. She take a random sample of size 49. The follow contingency table is constructed. Blood Donor Status Yes No Total Men Women Total What are the hypotheses? H 0 : p y = p n vs. H 1 : p y p n 2. What is the test statistic? χ 2 = What are the degrees of freedom? DF = (#r 1)(#c 1) = (2 1)(2 1) = 1 4. What is the pvalue? pvalue = Should you reject the null hypothesis (decision)? Is pvalue < α? No; do not reject H 0 6. What conclusion can we draw from this test? There is evidence that status and gender are independent. 7. What is the expected value for cell row 2 column 2? E 2,2 =
10 2.10 SLR Scenario 6 A statistician for an American automobile manufacturer would like to develop a statistical model for predicting delivery time (the days between initiating the order to the actual delivery of the new car) of customordered new automobile. The statistician believes there is a linear relationship between the number of options ordered on a car and the delivery time. A random sample of 16 cars is selected with the following results. Options Ordered vs Delivery Time Regression Statistics Multiple R R square Adj R sq Standard error Observations 16 Delivery Time Residuals Residuals vs Fitted Options Ordered Fitted values lm(time ~ Options) ANOVA df SS MS F Significance F Regression Residual Total Coefficients Coefficient Std error t Stat pvalue Low 95% Up 95% intercept optionsordered Identify which variable is the X, independent, or explanatory variable. Options is the independent variable. 2. Identify which variable is the Y, dependent, or response variable. Time is the dependent variable. 3. Describe the pattern of points as they appear on the graph. As options increases, time increases. 4. What kind of relationship do you see? The relationship is positive and linear. 10
11 5. Are there any outliers? There are no apparent outliers. 6. Describe the strength and direction of the correlation. The strength of the correlation is strong (r =.98) and the direction is positive. 7. Compare this relationship with the pattern of points on the scatter diagram between the two variables. They are in agreement. 8. Write the specific estimated regression equation for this problem. time = b 0 + b 1 (options) = options 9. Using the estimated regression equation predict the average delivery time for the average car with 16 options ordered. time = = Is the previous prediction extrapolation? No, since the minimum options is 3 and the maximum options is Interpret the slope estimate, that is, explain what is means in terms of this problem. As options increases by one, time increases by 2.07 days (i.e., value of the slope). 12. Determine the coefficient of determination or how much variation in delivery time is accounted for by this regression model? Express your answer as a percent. What measure did you use to answer this question? Coefficient of determination = r 2 = 95.75%. 13. What is the standard error of the estimated regression line? Include the unit of measurement in your answer. s = days. 14. Using a 5% level of significance, is there evidence of a linear relationship between delivery time and options ordered? Be sure to state the hypotheses, test statistic, pvalue, and the conclusion. H 0 : β = 0 vs. H 1 : β 0 t = pvalue = 0 There is evidence that the slope is not zero. 11
12 15. Give a 95% confidence interval for the true (i.e., population) slope. (1.819, ) is a 95% confidence interval. 16. If the original correlation coefficient between these two variables were not known, how could it be calculated using the statistics in the regression output? How do you determine the sign of the correlation coefficient? r = r 2. The sign of r is determined by the sign of the slope. 17. Describe what you see on the residual plot. There appears to be a slight pattern. 18. For the data set, look at the 9 th pair of observations (Options, Time) or (12, 44). Calculate the residual, i.e., e i = Y i Ŷi. e 9 = 44 ( ) = = Is the model a good fit for the data? Be sure to state your decision and give the reasons that support your decision. Consider the following: r 2 =.9785 s = days Rejected H 0 of the slope. Review the scatter plot 12
13 2.11 MLR Scenario 7 Suppose a consumer organization wanted to develop a model to predict gasoline mileage as measured by miles per gallon (MPG) based on the horsepower of the car s engine and the weight of the car. A sample of 50 recent car models was selected, with the results summarized below. Regression Statistics Multiple R R square Adj R sq Standard error Observations 50 Correlation Coefficient MPG HP WT MPG 1 HP WT Descriptive Statistics MPG Horsepower Weight Mean Std Err Std Dev Variance Minimum Maximum Sum Count Min  Max xvariable Min Max HP WT ANOVA df SS MS F Significance F Regression Residual Total Coefficients Coefficient Std error t Stat pvalue Low 95% Up 95% intercept Horsepower Weight Identify which variables are the X, independent, or explanatory variables. Horsepower (HP) and weight (WT) are the explanatory variables. 2. Identify which variable is the Y, dependent, or response variable. Miles per gallon (MPG) is the response variable. 13
14 3. Describe the strength and direction of the correlation. Correlation coefficient between MPG and HP is Correlation coefficient between MPG and WT is Correlation coefficient between WT and HP is Write the specific estimated regression equation for this problem. MP G = HP W T 5. Using the estimated regression equation predict the average MPG for a car that has 60 HP and weighs 2000 lbs. MP G = = 37.3mpg 6. Is the previous prediction extrapolation? No; since HP = 60 is between 48 and 165 and WT = 2000 is between 1755 and Interpret the slope estimate, that is, explain what is means in terms of this problem. Holding WT constant, as HP increasing be one, MPG decreases by Holding HP constant, as WT increasing be one, MPG decreases by Determine the coefficient of multiple determination or how much variation in MPG is accounted for by this regression model? Express your answer as a percent. What measure did you use to answer this question? r 2 = 74.9% 9. What is the standard error of the estimated regression line? Include the unit of measurement in your answer. s = mpg. 10. Using a 5% level of significance, is there evidence of a linear relationship between MPG and the explanatory variables? Be sure to state the hypotheses, test statistic, pvalue, and the conclusion. H 0 : β 1 = β 2 = 0 vs. H 1 : at least one β i 0 where i = (1, 2) 11. Give a 95% confidence interval for the true (i.e., population) slope of MPG and HP. A 95% confidence interval for MPG and HP is (.1832, ). 14
15 12. For the data set, look at the 1 st set of observations (MPG, HP, WT) or (43.1, 48, 1985). Calculate the residual, i.e., e i = Y i Ŷi. e 1 = 43.1 ( ) = = Is the model a good fit for the data? Be sure to state your decision and give the reasons that support your decision. r 2 =.7494 s = Rejected H 0 Questions Questions? 15
Final 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 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 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 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 informationSimple 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 Statistical model for linear regression Estimating
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationPremaster Statistics Tutorial 4 Full solutions
Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for
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 informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationNull Hypothesis H 0. The null hypothesis (denoted by H 0
Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property
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 informationSELFTEST: SIMPLE REGRESSION
ECO 22000 McRAE SELFTEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an inclass examination, but you should be able to describe the procedures
More informationE205 Final: Version B
Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random
More informationStatistics for Management IISTAT 362Final Review
Statistics for Management IISTAT 362Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to
More informationChapter 11: Two Variable Regression Analysis
Department of Mathematics Izmir University of Economics Week 1415 20142015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions
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 informationChapter 9, Part A Hypothesis Tests. Learning objectives
Chapter 9, Part A Hypothesis Tests Slide 1 Learning objectives 1. Understand how to develop Null and Alternative Hypotheses 2. Understand Type I and Type II Errors 3. Able to do hypothesis test about population
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 informationThe scatterplot indicates a positive linear relationship between waist size and body fat percentage:
STAT E150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the
More informationIn Chapter 2, we used linear regression to describe linear relationships. The setting for this is a
Math 143 Inference on Regression 1 Review of Linear Regression In Chapter 2, we used linear regression to describe linear relationships. The setting for this is a bivariate data set (i.e., a list of cases/subjects
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 informationPaired Differences and Regression
Paired Differences and Regression Students sometimes have difficulty distinguishing between paired data and independent samples when comparing two means. One can return to this topic after covering simple
More informationMultiple Regression in SPSS STAT 314
Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan
More informationTwosample hypothesis testing, II 9.07 3/16/2004
Twosample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For twosample tests of the difference in mean, things get a little confusing, here,
More informationACTM State ExamStatistics
ACTM State ExamStatistics For the 25 multiplechoice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tiebreaker
More informationOutline. Topic 4  Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4  Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test  Fall 2013 R 2 and the coefficient of correlation
More informationEstimation of σ 2, the variance of ɛ
Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated
More informationCHAPTER 2 AND 10: Least Squares Regression
CHAPTER 2 AND 0: Least Squares Regression In chapter 2 and 0 we will be looking at the relationship between two quantitative variables measured on the same individual. General Procedure:. Make a scatterplot
More informationElementary Statistics Sample Exam #3
Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to
More informationHypothesis testing  Steps
Hypothesis testing  Steps Steps to do a twotailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =
More informationHypothesis testing for µ:
University of California, Los Angeles Department of Statistics Statistics 13 Elements of a hypothesis test: Hypothesis testing Instructor: Nicolas Christou 1. Null hypothesis, H 0 (always =). 2. Alternative
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 information0.1 Multiple Regression Models
0.1 Multiple Regression Models We will introduce the multiple Regression model as a mean of relating one numerical response variable y to two or more independent (or predictor variables. We will see different
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 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 informationRegression in SPSS. Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology
Regression in SPSS Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology John P. Bentley Department of Pharmacy Administration University of
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 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 informationRegression III: Dummy Variable Regression
Regression III: Dummy Variable Regression Tom Ilvento FREC 408 Linear Regression Assumptions about the error term Mean of Probability Distribution of the Error term is zero Probability Distribution of
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 informationFactors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationResiduals. Residuals = ª Department of ISM, University of Alabama, ST 260, M23 Residuals & Minitab. ^ e i = y i  y i
A continuation of regression analysis Lesson Objectives Continue to build on regression analysis. Learn how residual plots help identify problems with the analysis. M231 M232 Example 1: continued Case
More informationInteraction between quantitative predictors
Interaction between quantitative predictors In a firstorder model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors
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 informationAugust 2012 EXAMINATIONS Solution Part I
August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the ttest
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One Way ANOVA Limitations of the ttest Although the ttest is commonly used, it has limitations Can only
More informationChapter 23. Inferences for Regression
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
More informationStatistics 112 Regression Cheatsheet Section 1B  Ryan Rosario
Statistics 112 Regression Cheatsheet Section 1B  Ryan Rosario I have found that the best way to practice regression is by brute force That is, given nothing but a dataset and your mind, compute everything
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationMultiple Regression Analysis in Minitab 1
Multiple Regression Analysis in Minitab 1 Suppose we are interested in how the exercise and body mass index affect the blood pressure. A random sample of 10 males 50 years of age is selected and their
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 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 informationStatistical Modelling in Stata 5: Linear Models
Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 08/11/2016 Structure This Week What is a linear model? How
More informationSimple 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 informationData and Regression Analysis. Lecturer: Prof. Duane S. Boning. Rev 10
Data and Regression Analysis Lecturer: Prof. Duane S. Boning Rev 10 1 Agenda 1. Comparison of Treatments (One Variable) Analysis of Variance (ANOVA) 2. Multivariate Analysis of Variance Model forms 3.
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 information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationp1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0.
Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested
More informationwhere b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.
Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes
More informationChapter 4 and 5 solutions
Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,
More informationAMS7: WEEK 8. CLASS 1. Correlation Monday May 18th, 2015
AMS7: WEEK 8. CLASS 1 Correlation Monday May 18th, 2015 Type of Data and objectives of the analysis Paired sample data (Bivariate data) Determine whether there is an association between two variables This
More information5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives
C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.
More informationBasic Statistcs Formula Sheet
Basic Statistcs Formula Sheet Steven W. ydick May 5, 0 This document is only intended to review basic concepts/formulas from an introduction to statistics course. Only meanbased procedures are reviewed,
More information1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ
STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material
More informationWe extended the additive model in two variables to the interaction model by adding a third term to the equation.
Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic
More informationRegression in ANOVA. James H. Steiger. Department of Psychology and Human Development Vanderbilt University
Regression in ANOVA James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) 1 / 30 Regression in ANOVA 1 Introduction 2 Basic Linear
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationIndependent t Test (Comparing Two Means)
Independent t Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent ttest when to use the independent ttest the use of SPSS to complete an independent
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 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 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 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 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 informationInterpreting Multiple Regression
Fall Semester, 2001 Statistics 621 Lecture 5 Robert Stine 1 Preliminaries Interpreting Multiple Regression Project and assignments Hope to have some further information on project soon. Due date for Assignment
More informationStatistics II Final Exam  January Use the University stationery to give your answers to the following questions.
Statistics II Final Exam  January 2012 Use the University stationery to give your answers to the following questions. Do not forget to write down your name and class group in each page. Indicate clearly
More informationUsing Excel for inferential statistics
FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationChi Square for Contingency Tables
2 x 2 Case Chi Square for Contingency Tables A test for p 1 = p 2 We have learned a confidence interval for p 1 p 2, the difference in the population proportions. We want a hypothesis testing procedure
More informationModule 5: Multiple Regression Analysis
Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College
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 informationOneWay Analysis of Variance (ANOVA) Example Problem
OneWay Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesistesting technique used to test the equality of two or more population (or treatment) means
More informationMULTIPLE REGRESSION EXAMPLE
MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if
More informationMath 62 Statistics Sample Exam Questions
Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected
More informationChapter 8 Introduction to Hypothesis Testing
Chapter 8 Student Lecture Notes 81 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate
More informationSupplement 13A: Partial F Test
Supplement 13A: Partial F Test Purpose of the Partial F Test For a given regression model, could some of the predictors be eliminated without sacrificing too much in the way of fit? Conversely, would it
More informationGeneral Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test
Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics
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 informationSIMPLE LINEAR CORRELATION. r can range from 1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.
SIMPLE LINEAR CORRELATION Simple linear correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables. Correlation
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
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 informationIntroduction to Stata
Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the midrange of how easy it is to use. Other options include SPSS,
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 Section 1 Homework Set A
Chapter 7 Section 1 Homework Set A 7.15 Finding the critical value t *. What critical value t * from Table D (use software, go to the web and type t distribution applet) should be used to calculate the
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 informationMath 130 Final Exam Spring 2014 \ NAME: . You must show all work, calculations, formulas used to receive any credit. NO WORK =NO CREDIT.
Math 130 Final Exam Spring 2014 \ NAME:. You must show all work, calculations, formulas used to receive any credit. NO WORK =NO CREDIT. Round the final answers to 3 decimal places. Good luck! Question
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationEPS 625 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM
EPS 6 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM ANCOVA One Continuous Dependent Variable (DVD Rating) Interest Rating in DVD One Categorical/Discrete Independent Variable
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10 TWOSAMPLE TESTS Practice
More informationTesting Hypotheses using SPSS
Is the mean hourly rate of male workers $2.00? TTest OneSample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 OneSample Test Test Value = 2 95% Confidence Interval Mean of the
More information