population multiple regression model with three independent varia ption of the CLM model. y = Bo + B₁x₁ + B₂X₂ + B3X3 + U you want to test the null hypothesis Ho: P₁ - 3B2 = 1 d ß₂ be the OLS estimators, respectively. Write Var(B₁ - the variances of B₁and B₂and the covariance between them. -statistic to test Ho: B₁-3ẞ2 = 1 = Bo - 3B₂, 0₁ B₁ - 382, Write a regression equation to get ₁a ectly.
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- The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of thenumber of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?IfX1 andX2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean μ and the variance σ ^2 , show that the variance of the unbiased estimator ω·Xbar1+(1−ω)·Xbar2is a minimum whenω=n1/(n1+n2)
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