16. Suppose the true average growth μ of one type of plantduring a 1-year period is identical to that of a secondtype, but the variance of growth for the first type is σ²,whereas for the second type the variance is 40². LetX₁,..., X be m independent growth observations on thefirst type [so E(X;) = µ, V(X;) = σ²], and let Y₁,..., Ybe n independent growth observations on the secondtype [E(Y) =μ, V(Y) = 4σ²].a. Show that the estimator û = 8X + (1 - 8) is unbi-ased for μ (for 0 < 8 <1, the estimator is a weightedaverage of the two individual sample means).b. For fixed m and n, compute V(u), and then find thevalue of 8 that minimizes V(i). [Hint: DifferentiateV(u) with respect to 8.]

###Part-a.To show that the estimator μ^=δXˉ+(1−δ)Yˉ is unbiased for μ, we need to demonstrate that…

Answered: 16. Suppose the true average growth μ…

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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2. Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature x (° F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y= 5 - 0.01x and the standard deviation o=0.075. a. What is the expected reaction time when temperature is 250° F? b. Suppose that five observations are made independently on reaction time, each one for a temperature of 250° F. What is the probability that all five times are between 2.4 and 2.6 hours?
Look at the following regression table where the dependent variable is the demand for illegal massage services in a city in the United States. Specifically, the dependent variable is the number of customers per hour (Models 1 and 2) or per day (Models 3 and 4). (a) Explain why the coefficient for Population/1,000 in Model 2 is very different from the one in Model 4?(b) Can you reject H0 in Model 1 if H0 : βP opulation/1,000 = 0.01, H1 : βPopulation/1,000 6= 0.01, and α = 0.01?
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
Suppose you are to estimate a simple regression for the following population model: Y=B₁ + B₁X + µl From a population of over thousands of observations, a small number of samples were randomly selected. The following is some of the information from the randomly selected sample.
13.1.1
The US government is interested in understanding what predicts death rates. They have a set of data that includes the number of deaths in each state, the number of deaths resulting from vehicle accidents (VEHICLE), the number of people dying from diabetes (DIABETES), the number of deaths related to the flu (FLU) and the number of homicide deaths (HOMICIDE). Your run a regression to predict deaths and get the following output: At α = .10, which variable(s) is/are significant predictors of deaths?
The following table gives the regression results of consumption behaviour between female and male. Consumption (C), in RM Model 1 Model 2 Constant 0.7515 0.6587 (0.024) (0.037) Y 0.8603 0.5442 (0.0301) (0.2881) Gen 0.2001 (0.0004) Y*Gen 0.3105 (0.0076) Adjusted R 0.78 0.78 No. of Observations 47 47 Note: Y=income (RM) Gen= Gender ( It is equal to 1 if person is female; 0 is for male) Figures in the parentheses are p- values a) Identify which are the qualitative, quantitative and interaction variable. Refer to Model 1: b) Write the regression equations for female and male. Draw the regression lines for female and male on the same diagram. What can you c) say? d) Interpret all the estimated slope coefficients. e) Conduct an appropriate test to determine whether variable gender is statistically significant at 5%. Should this variable be dropped from this regression model.
Here's a table with average monthly price of a stock from Jan 2021-July 2021. Month Price Jan 29000 Feb 27000 Mar 31000 Apr 30000 May 32000 June 28000 July 29000 Using a 3-period weighted moving average with weights (wt, wt-1, W-2) = (0.6, 0.2, 0.2), the predicted price August is Using an exponential smoothing model with = 0.4, and with the initial predicted price for Jan the same as the observed price for January, the predicted price for August is % Now, let's suppose that we finally observe that the price for August is 30000. The absolute percent error (APE) of your prediction for August is using the weighted moving average method and % using the exponential smoothing model. (Note: Round your answer to the nearest 2 decimal places. For your APE answer for example let's say you get 0.06786 from Excel, then you should type-in 6.79 as your answer here since it is represented as percentage. Do not enter any symbols other than integers and decimal.)
12. All coefficients in the following regressions are statistically significant. Which of these regressions represent a sensible choice in adjusting the respective multiples A. PE = 17 + (5*Growth) B. PB = 1+(2*ROE) C. PS= 3+(4*net profit margin) D. EV/ Capital = 2+( 5*ROC) - (3* growth)
18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0 at the α = 0.05 significance level (i.e. we want to determine if the addition of ethanol significantly decreases mean gas mileage). What is the p−value for this test? What is your conclusion? Note: s?e(βˆ1) = 0.0485. Which of the following is/are true? (A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol (B) In reference to question (18), a 95% confidence interval for β1…

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