Consider the following system of simultaneous regression equations: (1) Yi = a1 + agx; +azz; + E; x; = B1 + B2yi+ Z4 = Y1 + 72w; + Vi (2) (3) Assuming that all the parameters are non-zero, which of the following statements are true?
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- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents. xx 11.5 8.5 6.7 3.5 2.9 2.7 2.7 0.9 yy 14.1 11 10 7.3 6.7 6.4 6.4 4.7 Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. Round to 2 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons? Round to 3 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 5.8 thousand automatic weapons? Round to 3 decimal places..The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?2.state each of the five assumptions of the classical regression model (OLS) and give an intuitive explanation of the meaning and need for each of them
- If the equation of the regression line that relates hours per week spent in the tutor lab, x, to GPA, y, is y=2.1+0.28, then the best presdiction for the GPA of students who never go into the lab would be 2.1 True Or FalseIn an instrumental variable regression model with one regressor, Xi, andone instrument, Zi, the regression of Xi onto Zi has R2 = 0.1 and n = 50.Is Zi a strong instrument? Would your answer change if R2 = 0.1 and n = 150?We have been assigned to determine how the total weeklyproduction cost for Widgetco depends on the number ofwidgets produced during the week. The following modelhas been proposed:Y b0 b1X b2X2 b3X3 where X number of widgets produced during the weekand Y total production cost for the week. For 15 weeksof data, we found that SSR 215,475 and SST 229,228.For this model, we obtain the following estimated regressionequation (t-statistics for each coefficient are in parentheses):yˆ 29.7 19.8X 0.39X2 0.005X3(0.78) (0.62) (1.25)a For a 0.10, test H0: bi 0 against Ha: bi 0(i 1, 2, 3).b Determine R2 for this model. How can the high R2value be reconciled with the answer to part (a)?
- We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. RBI's HR's Salary (in millions) 108 38 28.050 86 31 27.500 59 25 25.000 119 31 25.000 103 39 24.050 44 15 23.125 49 11 23.000 111 30 22.750 87 31 22.125 90 18 21.857 49 7 21.667 70 21 21.571 108 35 21.500 56 9 21.143 84 38 21.119 80 14 20.802 17 7 20.000 79 24 20.000 91 31 20.000 97 29 20.000 57 13 18.500 44 8 18.000 104 32 18.000 86 27 18.000 100 25 17.454 62 20 17.000 58 20 17.000 100 29 16.083 127 38 16.000 83 29 16.000 59 30 16.000 54…We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Miquel Cabrera 108 38 28.050 Yoenis Cespedes 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez 111 30 22.750 Justin Upton 87 31 22.125 Adrian Gonzalez 90 18 21.857 Jason Heyward 49 7 21.667 Jayson Werth 70 21 21.571 Matt Kemp 108 35 21.500…Consider the following two a.m. peak work trip generation models, estimated by household linear regression: T = 0.62 + 3.1 X1 + 1.4 X2 R2= 0.590 (2.3) (7.1) (5.9) T = 0.01 + 2.4 X1 + 1.2 Z1 + 4.0 Z2 R2= 0.598 (0.8) (4.2) (1.7) (3.1) X1 = number of workers in the household X2 = number of cars in the household, Z1 is a dummy variable which takes the value 1 if the household has one car, Z2 is a dummy variable which takes the value 1 if the household has two or more cars. Compare the two models and choose the best. If a zone has 1000 households, of which 50% have no car, 35% have one car, and the rest have exactly two cars, estimate the total number of trips generated by this zone. Use the preferred trip generation model and assume that each household has an average of two workers
- If the points (x1, y1), (x2, y2),..., (xn, yn) lie on a straight line, what can you say about the regression line associated with these points?Q11. A fitted linear regression equation is ŷ = 6–2x. If x = 3 and the corresponding observedvalue of y = 2, the residual at this observation is:a. –5b. 2c. –3d. –2To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 Day Date Weekday Daily Demand Weekend 1 4/25/2016 Mon 297 0 2 4/26/2016 Tue 293 0 3 4/27/2016 Wed 327 0 4 4/28/2016 Thu 315 0 5 4/29/2016 Fri 348 0 6 4/30/2016 Sat 447 1 7 5/1/2016 Sun 431 1 8 5/2/2016 Mon 283 0 9 5/3/2016 Tue 326 0 10 5/4/2016 Wed 317 0 11 5/5/2016 Thu 345 0 12 5/6/2016 Fri 355 0 13 5/7/2016 Sat 428 1 14 5/8/2016 Sun 454 1 15 5/9/2016 Mon 305 0 16 5/10/2016 Tue 310 0 17 5/11/2016 Wed 350 0 18 5/12/2016 Thu 308 0 19 5/13/2016 Fri 366 0 20 5/14/2016 Sat 460 1 21 5/15/2016 Sun 427 1 22 5/16/2016 Mon 291 0 23 5/17/2016 Tue 325 0 24 5/18/2016 Wed 354 0 25 5/19/2016 Thu 322 0 26 5/20/2016 Fri 405 0 27 5/21/2016 Sat 442 1 28 5/22/2016 Sun 454 1 29 5/23/2016 Mon 318 0 30 5/24/2016 Tue 298 0 31 5/25/2016 Wed 355 0 32 5/26/2016 Thu 355 0 33 5/27/2016 Fri 374 0 34 5/28/2016 Sat 447 1 35 5/29/2016…