Consider an simple wage model:W₁ = BFdFi + BMd Mi + ε;where w is hourly wage and where dƑ is a dummy variable that equals 1 if the samplemember is female, and 0 otherwise; dò is a dummy variable that equals 1 if the samplemember is male, and 0 otherwise.Notice that this model has no constant term (which would make it impossible to estimate).Derive b = [b₁,b] for this model using the least squares formula b = (X'X)`¹X'Y.F(The result will be quite simple and intuitively reasonable. Show the steps.)

The wage model is given as follows: wi=βFdFi+βMdMi+εior, w=βFdF+βMdM+ε So, the hourly wage w is the…

Answered: Consider an simple wage model: W₁ =…

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 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 following table gives the quantity demanded of ice cream (Qic) in kgs per year in Sardinia (Italy), its price (Pic) in $ per kg, consumers’ income (I) in $, the temperature (T) in Celsius, and the price of cappuccino (Pc) in $ per kg: Year Qic Pic ($/kg) I ($) T Pc ($/kg) 2000 72000 11 2000 20 14 2001 81000 10 2100 24 15 2002 90000 9 2200 25 15 2003 99000 7 2305 26 16 2004 108000 6 2407 30 17 2005 126000 4 2500 32 18 2006 117000 7 2610 26 16 2007 117000 8 2698 25 16 2008 135000 5 2801 31 18 2009 135000 5 2921 31 18 2010 144000 4 3000 34 20 2011 180000 2 3099 36 21 2012 162000 5 3201 33 19 2013 171000 4 3308 35 21 2014 153000 6 3397 30 18 2015 180000 3 3501 35 22 2016 171000 4 3689 33 20 2017 180000 3 3800 36 23…
Suppose you believe that population abundance (A) of a particular species is a linear function of vegetation coverage (V) and the presence of a predators (P). Surveys where conducted across 20 sites and found the following information: a) There was an average of cover of .406 (40.6%) of the area, with an average 6.8 predators and 61.55 individuals in our target population. b) ⟨V2⟩=0.231⟨V2⟩=0.231, ⟨P2⟩=76.300⟨P2⟩=76.300, ⟨VP⟩=2.933⟨VP⟩=2.933, ⟨VA⟩=36.329⟨VA⟩=36.329, ⟨PA⟩=379.300⟨PA⟩=379.300 Set up the appropriate system of equations needed for a the linear regression of a model of the form A=aV+bP+cA=aV+bP+c. Then estimate the parameters and report the final model.
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): X 1= average high school grade in mathematics (HSM) X 2 = average high school grade in science (HSS) X 3 = average high school grade in English (HSE) X 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: SOURCE DF MS F VALUE PROB>F MODEL 28.64 5.73 11.69 0001 ERROR 218 106 82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN 0.700 R-SQUARE 0.211 4.635 ADJ R-SQ 0.193 PARAMETER STANDARD T FOR O VARIABLE ESTIMATE ERROR PARAMETER -0 PROB> ITI INTERCEPT 2.327 0.039 5.817 0.0001 0.0003 XI HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV) 0.146 0.037 3.718 a.036 0.038 0.950 0.3432…
Are the signs of the coefficients on the variables "Frequency of Flights" and "Destination is a Big City" corresponding to the utility of the "Air" mode meaningful? Utility for Car Utility for Air param. t stat Param. t stat Constant 4.77 6.995 0 fixed Travel Time (mins) -0.03 -16.926 -0.03 -16.926 Travel Cost / Income ($/$) -726.35 -4.28 -726.35 -4.28 Frequency of Flights (per week) 0 fixed 0.12 13.414 Is Destination a Large City 0 fixed 1.5 5.576 Travel Party Size > =2^2 1.75 5.873 0 Fixed
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y). The results were: Y a+bx b = -0.79 = 23.04 a r² = 0.4493 r = -0.6703 a. If a person watches 10 hours of television a day, predict how many sit-ups he can do. b. If a person can do 7 sit ups, predict how many hours of television a day they watch. hours
The variation of Y around its mean can be decomposed into which two parts?
Given the data points (1, 13), (4, 235), (8, 2974), and (10, 6875.5), find the value of f(x) if x = 3.21 using quadratic interpolation. Round off your final answer to five decimal places but do not round off in preliminary calculations. Answer: 24.21023
A regression was run to determine if there is a relationship between hours of TV watched per day (xx) and number of situps a person can do (yy). The results of the regression were: y=ax+ba=-1.392b=32.952r2=0.527076r=-0.726Use this to predict the number of situps a person who watches 2 hour(s) of TV can do, and please round your answer to a whole number.
A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable. T or F
The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant ŷ = 2.35+2.20X. Suppose, for a selected workstation, the labor input is 5, the predicted output is?
The table lists the average monthly cost to workers for family health insurance for various years. Year, x Average Monthly Cost to Workers for Family Health Insurance $298 a) Use a graphing calculator to fit a regression line to the data. b) Predict the average monthly cost to workers for family health insurance in 2020, and compare the value with $493.3, which is obtained using the points (1,340) and (4,386). c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely. 2009, 0 2010, 1 2011, 2 340 348 2012, 3 367 2013, 4 2014, 5 386 406 a) The linear equation of the regression line that best models the data is y =x+. (Round to the nearest hundredth as needed.) b) The average monthly cost to workers for family health insurance in 2020 is predicted to be $ (Round to the nearest cent as needed.) Compare the above obtained value with $493.3 This value is $ $493.3 c) The correlation coefficient is (Round to the nearest thousandth as…

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