The linear probability model‚ ctd. When Y is binary‚ the linear regression model Yi = β0 + β1Xi + ui is called the linear probability model. • The predicted value is a probability: • E(Y|X=x) = Pr(Y=1|X=x) = prob. that Y = 1 given x • Yˆ = the predicted probability that Yi = 1‚ given X • β1 = change in probability that Y = 1 for a given ∆x: Pr(Y = 1 | X = x + ∆x ) − Pr(Y = 1 | X = x ) β1 = ∆x 5 Example: linear probability model‚ HMDA data Mortgage denial v. ratio of debt payments to income (P/I
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shipment‚ five chips are chosen at random. What is the probability that none of them is defective? What is the probability that at least one is defective? 2. An automated manufacturing process produces a component with an average width of 7.55 centimeters‚ with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter from the mean must be rejected. What percentage of parts must be rejected? Assume a normal distribution. 3. Assume that the number of cases sold per
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Use this probability to calculate the approximate number of packets containing no defective‚ one defective and two defective pens‚ respectively in a consignment of 20‚000 packets [ e^(--0.02) =0.9802 ] Ans. : 19604‚ 392‚ 3.92=4 respectively 2. A manufacturer who produces medicine bottles finds that 0.1% of the bottles are defective. The bottles are packed in the boxes of 500 bottles. A drug manufacturer buys 100 boxes from the producer of bottles . Using suitable probability distribution
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2010 Words of Probability ISHIGURO‚ Makio(The Institute of Statistical Mathematics) Words of Probability ISHIGURO‚ Makio(The Institute of Statistical Mathematics) Key Words: subjective probability‚ confidence‚ belief‚ frequency‚ verbal expression Abstract There are everyday expressions such that ’probably’; ’might be’;’could be’ etc.‚ to describe the strengths of one’s confidence in the occurrence of events in the future. On the other hand there are probability theory expressions
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Probability Paper David E. Nelson QNT/561 February 14‚ 2013 Professor Minh Bui Probability Paper My friends suggested that we take a hiking trip through South America this year. The reason for such a trip was to celebrate 16 years of close friendship. The four of us had known each other since we were in middle school and have since become inseparable. Even though we all lead very different lives and have even started our own families‚ we always manage to find time to spend with each other
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10/10 (11am-3pm). PART I. MULTIPLE CHOICES 1. Circle your answers on the exam. 2. Copy your answers to a SCANTRON sheet. PART II. WORK PROBLEMS 1. Give neat‚ clean‚ and well organized answers. 2. Support your answers. *This set of problems may take more than 4 hours to solve. The purpose is to provide you a set of problems for practice. Part I: Multiple Choice (50 Questions) Identify the letter of the choice that best completes the statement or answers the question
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2013 Rich Haller Statistics in Business Statistics is a way of gathering‚ analyzing‚ interpreting and presenting data so that it becomes more meaningful. It helps convert raw data into useful information. Statistics is therefore a collection of information. Statistics can be presented in graphical form to make it more appealing and easily understandable by the users. Statistics can be descriptive or inferential. Descriptive statistics have to do with methods in a data set that utilizes numerical
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Chapter 2: Descriptive Statistics CHAPTER 2: Descriptive Statistics 2.3 [LO 1] 28 2007 #1 28 71‚273.93 58‚069‚987.70 7‚620.37 59490 87970 28480 Distribution is skewed right. Descriptive statistics count mean sample variance sample standard deviation minimum maximum range Stem and Leaf plot for stem unit = leaf unit = Frequency 2 9 13 4 28 #1 10000 1000 Stem 5 6 7 8 Leaf 99 123446677 0000112444447 1377 Distribution is more normally shaped in 2007. 2.5 [LO 2] a. We have 2
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Probability theory Probability: A numerical measure of the chance that an event will occur. Experiment: A process that generates well defined outcomes. Sample space: The set of all experimental outcomes. Sample point: An element of the sample space. A sample point represents an experimental outcome. Tree diagram: A graphical representation that helps in visualizing a multiple step experiment. Classical method: A method of assigning probabilities that is appropriate when all the experimental
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Organization of Terms Experimental Design Descriptive Inferential Population Parameter Sample Random Bias Statistic Types of Variables Graphs Measurement scales Nominal Ordinal Interval Ratio Qualitative Quantitative Independent Dependent Bar Graph Histogram Box plot Scatterplot Measures of Center Spread Shape Mean Median Mode Range Variance Standard deviation Skewness Kurtosis Tests of Association Inference Correlation Regression Slope y-intercept
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