3. Consider the vectorB1B =B2with variance-covariance matrixVar(B,)Var(ß) = ( Cov(B1, B2)Cov (β, β )Var(8,))and the matrix3 -1A =1Show – for this example – that Var(AB) = AVar(B)A'.

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Answered: 3. Consider the vector B1 B = B2 -(A)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
For each of the correlations respond with the following (Revise*Anxiety, Revise*Exam, and Anxiety*Exam) 1. Was the correlation significant? 2. Report the results in APA format
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The correlation matrix between the potential explanatory variables is given: 1 - 0,94 - 0,40 - 0,90 0,69 - 0,94 1 0,59 0,92 -0,56 R= -0,40 0, 59 1 0,35 -0,49 - 0, 35 0, 35 - 0,56 - 0,49 - 0, 35 -0,90 0,92 1 0,69 1 Determine the critical correlation coefficient based on the minimax rule.
We are researching the charity donation behaviour of Australians. We have the following model: (E1) Donate = β0 + β1Income +β2Avg_Gift + β3Edu + u Where: Donate is a dummy variable equal to 1 if the individual makes a donation in response to a social media campaign by our charity organisation, and 0 otherwise Income is the annual household income Avg_Gift is the average value of past donations made by the individual to our charity Educ is the individual's level of education (in years) Our data is a random sample of the population and we have 1,614 observations. You should assume E [u | Income, Avg_Gift, Educ] = 0. Using the information above, please answer the following 3 questions. [i] Referring to Model (E1) above, interpret the coefficient β1. [ii] You know that this model will suffer from heteroskedasticity. Why is this the case? Explain your reasoning. [iii] In your own words, what is heteroskedasticity?

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3. Consider the vector B1 B = B2 -(A) with variance-covariance matrix Var(B) Cov(B1, B2) Cov(B1, B2) Var(B2) Var(3) = and the matrix (:구) 3 -1 A = 1 Show – for this example – that Var(Aß) = AVar(B)A'.