For an AR(1) model with Y = 7.5, ø = -0.6, µ = 5, and o? = 1, %3| %3D (a) Find Ý(1), Ý;(2), and Ý-(6). (b) Find the error variances for your forecasts above.
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- For the regression model Yi = b0 + eI, derive the least squares estimator.Imagine a family member looks over your shoulder as you look at the variance equation Σki=1(xi − μ)2P(X = xi) and asks why the P(X = xi) term is there. What would you say?There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How would I derive LSE for B0 and B1 and their variance?
- Compute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) testIf the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
- Two lines of regression are given by 5x+7y-22=0 and 6x+2y-22=0. If the variance of y is 15, find the standard deviation of x.Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?A portfolio with a beta of 0.7 with market and residual variance of 10, market variance being 196 , the total risk in terms of standard deviation of the fund is a. 10.30 b. 14 c. 10 d. 7
- Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentFor some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m1 is the frequency at age t1, and m2 is the frequency at age t2, then the yearly rate of increase is estimated by r = (m2 − m1)/(t2 − t1). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per μgDNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per μg DNA. Assume that age is measured with negligible uncertainty.a) Estimate the yearly rate of increase, and find the uncertainty in the estimate.b) Find the relative uncertainty in the estimated rate of increase.The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.