Considering the following MA(3) process: y_t = u_t − 0.7u_(t-1) − 0.2u_(t-2) + 0.4u_(t-3) Where u_t is a white noise process with variance equal to 1. What is the value epsilon_k = cov(y_t,y_(t-k)) for k = 0?  Provide the correct answer along with the working steps and underlying assumptions used to c

Researches are interested in whether or not the average fuel economy for compact cars is thesame as sedan cars. A sample of 36 compact cars and 25 sedan cars is taken.The sample of compacts returns a mean of ̄X = 38 miles per gallon and sample variance of s^2 = 25.The sample of sedans returns a sample mean ̄Y = 36 with a sample variance of s^2 = 49.Let μ 1 be the population mean of compacts and μ 2 for sedans. a. Create a 95% confidence interval for μ 1 .b. Now create a 95% confidence interval for μ 1 μ 2 .c. Say the interval from part b. contains 0. What can you say about the difference in the averagefuel economy of compact cars versus economy cars

HI,  I'm doing a regression output with Hayes Model 1 Based on the information below the 95% CI [-.6020, .065] is statistically significant but the p = .114 is this a correct assumption? (b1) of -.268, t = -1.58, p = .114, 95% CI [-.6020, .065]. I asked this question originally with the wrong numbers sorry I corrected it... thank you

We calculate the correlation between the percent of adult population fully vaccinated for COVID-19 and the COVID-19 death rate per 100,000 in 2021 for the states and territories of the United States (55 observations). We observe a correlation r=-0.3558 Test the hypothesis H_0: ρ=0 against H_a: ρ≠0 at the 99% level (α=.01)

5 How does the dynamic CCE estimator solve the estimation problems of the PMG technique?

Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2  according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…

Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than  standard plastics. The accompanying data on melting point (°C) for each of 12 specimensof the polymer using a differential scanning calorimeter appeared in the article “The Melting Behaviour of Poly (3-Hydroxybutyrate) by DSC. Reproducibility Study” (Polymer Testing, 2013: 215-220).   Compute the following:a. The sample rangeb. The sample variance s2 from the definition [Hint: First subtract 180 from each observation.]c. The sample standard deviationd. s2 using the shortcut method