Dec 8 2005 ECON 240A 1 Final L Phillips Answer all five questions They are weighted equally 1 30 We examined the lottery data file xr 18 in labs 6 and 7 Exploratory data analysis is an important tool in illustrating the zeros problem and thereby avoiding the econometric problem of bias in estimating a multivariate regression of percent of household income spent on the lottery as explained by income education age and number of children the incorrect methodology that was suggested in the text in problem 18 13 The stem and leaf diagram of percent of household income spent on the lottery is shown in Figure 1 1 and the histogram is illustrated in Figure 1 2 Figure 1 1 Stem Leaf Display Percent of Household Income Spent On Lottery Stems 0 1 Leaves 0000000000000000000000011122333333455555555566666677777777777777778888888888888899999 000000001111123 a How many zeros are there 23 Dec 8 2005 ECON 240A 2 Final L Phillips b Is the distribution unimodal No there is a mode at zero and a second mode at 7 i e there are probably two peaks The box plot is shown in Figure 1 3 Figure 1 3 Box Plot of Percent of Household Income Spent On lottery Lottery Smallest 0 Q1 1 Median 6 5 Q3 8 Largest 13 IQR 7 Outliers c Is the median in the middle of the inter quartile range No median is 6 5 and Q1 1 and Q3 8 so the median is much closer to Q3 d One fourth of the observations lie below what value Below or equal to Q1 1 From the stem and lea diagram the smallest 25 observations consist of 23 zeros and 2 ones e What methodologies alternative to multivariate regression might you suggest You could convert the dependent variable to zeros and ones and estimate a probability model linear logit probit estimate a Tobit or estimate a count model 2 30 The data for percent of household income spent on the lottery and years of educational attainment sorted by the latter is exhibited in Table 2 1 Table 2 1 Dec 8 2005 Lottery Education ECON 240A 3 Final L Phillips Dec 8 2005 0 5 9 3 6 7 10 13 7 7 7 8 8 10 10 10 10 11 11 12 0 6 6 7 7 7 7 8 9 10 10 0 0 3 3 7 8 8 8 8 8 9 10 11 0 5 7 8 ECON 240A 4 Final 7 7 7 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 L Phillips Dec 8 2005 8 8 9 11 11 0 6 2 4 5 5 7 7 7 7 8 8 9 5 5 5 6 7 0 0 0 0 0 0 0 1 2 3 5 6 0 0 0 0 1 1 3 3 5 7 8 0 0 ECON 240A 5 Final 12 12 12 12 12 13 13 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 18 18 L Phillips Dec 8 2005 0 0 0 0 ECON 240A 6 Final L Phillips 19 19 20 20 a How many people with educational attainment from 7 11 years play the lottery 40 b How many people with educational attainment from 7 11 years do not play the lottery 4 c Fill in the boxes in Table 2 2 the number of players and non players for three categories of educational attainment Table 2 2 Cross Classification of Players and Non Players by Educational Level Educational Level in Years 7 8 9 10 11 Players Non Players Marginal 40 4 44 12 13 14 15 16 17 18 19 20 Marginal 25 2 27 12 17 29 77 23 100 d Fill in the expected numbers under the null hypothesis of independence between playing the lottery or not and educational level in Table 2 3 Table 2 3 Number of Players and Non Players By Educational Level Assuming Independence Educational Level in Years 7 8 9 10 11 Players Non Players Marginal 33 88 10 12 12 13 14 15 16 17 18 19 20 Marginal 20 79 6 21 22 33 6 67 100 e Fill in the contribution to Chi Square in the six boxes in Table 2 4 Dec 8 2005 ECON 240A 7 Final L Phillips Table 2 4 Contribution to Chi Square Educational Level in Years 7 8 9 10 11 Players Non Players 12 13 14 15 16 17 18 19 20 1 11 3 70 0 85 2 85 4 78 16 0 f With the probability of a type I error equal to 5 what is the critical level of Chi Square beyond which the sum of the six boxes in Table 2 3 will lead you to reject the null hypothesis of independence There are two degrees of freedom The critical value of chi square for twodegrees of freedom above which 5 of the distribution lies is 5 99 3 30 The Challenger data used for Takehome Project I showed launch temperatures ranging from 53 degrees Fahrenheit to 81 degrees Fahrenheit This temperature range can be divided into approximately three equal ranges 530 610 620 710 and 720 810 Three dummy variables were created for each temperature range DUMLOW DUMMED and DUMHIGH The number of o ring failures per launch was regressed against these three dummy variables Dec 8 2005 ECON 240A 8 Final L Phillips The data for number of failed o rings per launch launch temperature and the three dummy variables is displayed in Table 3 1 Table 3 1 Number of O Ring Failures Per Launch and Launch Temperature ORINGS 3 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 TEMP 53 57 58 63 66 67 67 67 68 69 70 70 70 70 72 73 75 75 76 76 78 79 80 81 DUMLOW 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 DUMMED 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 DUMHIGH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 The regression results from regressing the number of failed o rings per launch against these three dummy variables for temperature range are displayed in Table 3 2 Table 3 2 Regression of Number of Failed O Rings Per Launch Versus Dummy Variable for Temperature Range Low Medium and High Dependent Variable ORINGS Method Least Squares Sample 1 24 Included observations 24 Variable Coefficient Std Error t Statistic Prob …
View Full Document
Unlocking...