Economists use Lorenz curves to illustrate the distribution of income in a country. Letting x represent the percent of families in a country and y the percent of total income, the model y = x would represent a country in which each family had the same income. TheLorenz curve, y = f(x), represents the actual income distribution. The area between these two models, for 0 sxs 100, indicates the "income inequality" of a country. In 2013, the Lorenz curve for a country could be modeled byy = (0.00068x2 + 0.0140x + 1.723)2, OSx S 100where x is measured from the poorest to the wealthiest families.(a) Find the income inequality (in dollars) for that country in 2013. (Round your answer to two decimal places.)(b) Use the Lorenz curve to complete the table, which lists the percent of total income earned by each quintile in the country in 2013. (Round your answers to three decimal places.)QuintileLowest2nd3rd4thHighestPercent

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Answered: Economists use Lorenz curves to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following table shows the average yearly tuition and required fees, in dollars, charged by four-year American private universities in the school year beginning in the given year. Date Average tuition 2012 $27,870 2013 $29,004 2014 $30,138 2015 $31,272 2016 $32,406 (a) Show that these data can be modeled by a linear function. For each change of 1 year in time there is an increase of $ in tuition. Find its formula. (Let d be the date in terms of number of years since 2012 and T tuition in dollars.) T(d) = 27,870+1134d (b) Plot the data points and add the graph of the linear formula you found in part (a). (c) What prediction does this formula give for average tuition and fees at four-year American private universities for the academic year ending in 2018?$
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The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.4 8 6.8 3.4 2.4 2.2 2.4 0.4 y 13.5 10.7 10.1 6.9 5.9 5.6 6.3 4.2 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation y = 0.85x + 3.97. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons? Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 4.3 thousand automatic weapons? Answer= Answer = Round to 3 decimal places.
The number of banks in a country has been dropping steadily since 1984, and the trend in recent years has been roughly linear. The annual data for the years 1999 through 2008 can be summarized as follows, where x represents the years since 1990 and y the number of banks, in thousands. n=10 Ex-235 ²-5605 Ey-77.564 Ey²=603.80424 Exy-1810.155 a. Find an equation for the least squares line. b. Use your result from part a to predict the number of banks in the year 2020. c. If this trend continues linearly, in what year will the number of banks drop below 6200? d. Find and interpret the correlation coefficient.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.9 8.4 6.6 3.8 2.6 2.3 2.2 0.9 y 14.2 11.1 9.6 7 6.2 6.1 5.8 5 x = thousands of automatic weaponsy = murders per 100,000 residentsThis data can be modeled by the equation y=0.85x+4.03. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 7.7 thousand automatic weapons?
9 students were surveyed to see what their age is and what their income level is. Find the equation of the line using linear regression. We want to predict their age using their income. age 18 24 38 22 19 35 28 19 27 income 456 786 835 855 645 244 587 1400 975 Just a side note, the 19 year old is making 1400, would be considered an outlier since they are making way more than everyone else. (y=-.0061x+34.9874 4 decimals) y=30.3709-.0064
A biscuit production manager wants to investigate the linear relationship between the number of items produced and the production cost. To pursue his/her objective, the manager recorded the data on the number of items produced per day and the production cost per day (in thousands of Malaysian Ringgit) as shown in Table 3 Table 3 Days 1 2 4 6. 7 8 10 11 Number of items, (x) 26 67 86 17 10 44 53 40 77 80 20 20 Production cost, (y) 21 60 69 47 50 | 98 39 55 85 104 37 20 a) Name the TWo (2) most popular correlation coefficients. OPearson Oz-table OT-table Ochi-square Ospearman b) Calculate the correlation coefficient, r. ху x2 y2 26 21 676 44 60 2640 1936 3600 53 69 3657 2809 4761 47 1880 2209 77 50 3850 5929 2500 80 98 7840 6400 9604 20 39 780 400 1521 20 55 1100 400 3025 67 5695 4489 7225 86 104 8944 7396 10816 17 37 629 289 1369 10 20 200 100 400 E y² = Σχ ΣΥ- Σχy- Ex? = || || **Answer should be up to 4 decimal place (dp) r = c) Based on the correlation coefficient, robtained, make a…
I just need the d section
The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded × 1000 hectares X₂ AGE - how long the farm has been in operation in years X3 = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ŷ INCOME the income per year recorded in × R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 a. C. Standardized Residual Sample Quantiles 15 1.0- 0.8- 0.6- 0.4- 0.2- 0.0- 20 SIZE X₁ 25 5 8 2 1.2 1.5 Predicted Theoretical Quantiles. 45 AGE X₂ 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed.…
Which of the following statements best describes linear regression? A measure of the degree of dependence between two variables. A statistical technique using pairs of data and identifying a line which ‘best fits’ all of the pairs of observations. A measure of the proportion of changes in the dependent variable which can be explained by a change in the independent variable. Shows individual costs against their associated activity levels but makes no attempt to identify a linear relationship between them.

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