Aur 2.81-0.23xgy, R² = 0.36, SER=0.78 (0.12) (0.04) that the estimator has a normal distribution, the 95% confidence interval for the slope is approximately the interval: .57, 3.05).
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- You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between wages paid (x) and profits can be modelled by the equation Profit = 25x − 0.1x2 + 200. Use a Nonlinear Solver tool to determine the level of wages that will maximize profits.A researcher has a sample of 6 annual observations {94, 104, 102, 99, 111 and 107} for the CPI in country Z for the period 2015 to 2020, and wants to forecast CPI for the years 2021, 2022 and 2023. The researcher uses 3 different forecasting models: A, B and C. Model A is an AR(1) model with no drift and with an estimated autoregressive coefficient = 0.7. Model B is a MA(1) model with no constant and with an estimated MA coefficient = -0.4 (note the minus !). Model C is a random walk model with no drift. The error terms over the 2015-2020 period were estimated to have the values: {3, -1, 2, 4, -3, 1}. a. Compute the 2021, 2022 and 2023 forecasted values for the consumer price index based on the three models. Show the formulas and the details of your calculations, and explain all the related symbols. b. Suppose that the actual values of the CPI over the 2021, 2022 and 2023 were {108, 114, 105}. Calculate the Root mean square error of the three model forecasts over the 2021-2023…The image is showing the estimation of the model with quarterly car sales in the U.S. from 1975 to 1990. Based on the parameter estimates, what is the predicted effect of a 10% increase in price on the number of cars sold? What would be the effect of that price increase on the value of car sales?
- Suppose that you have the following model and data to estimate the following equation; Nobs Y X2 X3 1 1 1 3 2 2 2 2 3 4 4 5 4 3 3 4 5 2 5 1 Find the OLS estimators for the parameters using the matrices above.We have a pooled cross section of data with data from 2009 and 1999 on women’s wages and their years of education. We consider the model: wage = β0 + β1Year2009 + β2educ + β3Year2009 × educ + u where wage is the hourly wage and educ is the years of education. Year2009 is a dummy variable equal to 1 in the year 2009 and 0 otherwise. Which of the following measures the change in the effect of education on the wage between 1999 and 2009? a) β0 b) β1 + β2 + β3 c) none of these answers d) β1 + β3 e) β3What is the model constant when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1? a. Ŷ = 4 + 8x1 + 3x2 b. Ŷ = 7 + 6x1 + 5x2 c. Ŷ = 4 + 8x1 + 3x2 + 4x1x2
- Ten economists were asked to predict the percentage growth in the Consumer Price Index over the next year. Their forecasts were as follows: 3.6 3.1 3.9 3.7 3.5 3.7 3.4 3.0 3.7 3.4 a. Compute the sample mean. b. Compute the sample median. c. Find the mode.A sample of subjects were asked their opinion about refurbishing the subway in New York (support, oppose). For the explanatory variables gender (female, male), religious affiliation (Protestant, Catholic, Jewish), and political party affiliation (Democrat, Republican, Independent), the model for the probability π of supporting legalized abortion, logit(pi) = alpha + betagh + betari + betapj has reported parameter estimates (setting the parameter for the last category of a variable equal to 0.0 and alpha^ = -0.11, beta^g1 = 0.16, beta^g2 = 0.0, beta^r1 = -0.57, beta^r2 = -0.66, beta^r3 =0.0, beta^p1 =0.84, beta^p2 = -1.67, beta^p3 =0.00) . Interpret how the odds of supporting refurbishment depend on gender. Find the estimated probability of supporting refurbishment for (i) male Catholic Republicans and (ii) female Jewish Democrats. If we defined parameters such that the first category of a variable has value 0, then what would beta^g2 equal? Show then how to obtain the odds ratio that…Suppose you run a regression y=alpha + beta*x + u. You know that the estimated coefficient is 2.94 and the standard error is 1.09. What is the value of t-statistic for your estimated coefficient beta?
- The management of a large firm would like to know something about employee morale and the other variables to which it may be related. To study these relationships, each employee in a simple random sample of 27 employees is interviewed and tested to obtain information concerning morale level and the average number of satisfying extra work social contacts experienced during a week. Whether or not the duties the employee usually performs are appropriate to the job title is also determined. The dependent variable Y is measure of morale, the quantitative independent variable, X1 is average number of social contacts, and the following dummy variable coding is used to quantify the qualitative variable: X2 = 1 if yes, X2 = 0 if no. The model including dummy variable and the interaction term was being estimated and a part of computer outputs is below: beta std error t p-value 95% CI for B Lower bound Upper bound Constant 260 134.308…A statistics instructor asks each student in his classes to report how much the student spent on textbooks for the semester. The figures reported by students are shown below. 725 735 555 420 385 480 505 270 405 285 585 450 515 560 500 395 545 595 365 455 505 345 555 485 560 475 520 455 355 590 550 495 505 505 495 465 370 355 480 385 515 605 480 410 485 560 475 350 465 435 455 380 320 535 565 520 510 495 485 650 490 295 555 540 565 490 570 380 610 600 390 375 390 335 525 445 540 490 485 555 440 560 405 590 520 470 560 510 340 385 585 635 415 455 590 385 505 510 545 405 470 560 495 515 495 595 565 615 470 680 465 470 310 470 505 465 375 360 650 460 560 500 375 500 370 415 490 440 470 525 535 640 385 475 425 595 505 365 485 495 390 380 585 690 Treat the data above as POPULATION data. 1 The mean expenditure on textbooks by all students is: a $485.38 b $495.29 c $505.40 d $515.71How can we say that Sample Average is the Efficient Linear Estimator of E(Y)?