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- Book Pages (x) Price (y) A 500 $7.10 B 700 7.60 C 750 9.10 D 590 6.60 E 560 7.60 F 650 7.10 G 475 5.10 (a) Develop a least squares estimated regression line. (Round your numerical values to three decimal places.) (b) Compute the coefficient of determination. (Round your answer to four decimal places.) Explain its meaning. (Give your answer as a percent. Round your answer to two decimal places.) The value of the coefficient of determination tells us that % of the variability in |--?-- ☑ has been explained by the least squares regression equation.Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
- The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2012 2010 2012 2014 2016 336.5 363.5 398.1 Year CO, Emissions 2018 424.8 451.1 Year 2022 2024 2026 2028 2030 Co, Emissions 559.2 591.9 628.7 665.1 707.1 2020 2032 743.7 Using x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions, write the equation of the linear function that models these data. (Round all numerical values to two decimal places.) Hint: Let x 0 in 2010. y(x) =Suppose that you wish to estimate the effect of class attendance on student performance. A basic model is examscore = β0 + β1attendance + β2priorGP A + u where examscore is students’ score on the exam (from 1 to 6), attendance is the number of TA sessions attended on Zoom (from 0 to 9), and priorGPA is the average exam grade last year. (a) Let internet be the quality of internet at the student’s study place. Do you think internet satisfies the independence assumption? What about the exclusion restriction? (b) Assuming that internet satisfies the conditions above, what other condition must internet satisfy in order to be a valid IV for attendance? (c) Suppose, we add the interaction term priorGP A × attendance. Interpret the coefficient on the interaction term. (d) (Difficult) If attendance is endogenous, then, in general, so is priorGP A × attendance. What might be a good IV for priorGP A × attendance?Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.
- ARCH(1) model o? = w+ ae?_1. Define Y; = e? and u: = e? – o?. %3D Show that Y, can be written as a specific autoregressive process with innovation u.Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: y USE SALT 2= Σχ = 15; Σy = 88.3; Σx2 = 55; Σy2 = 1,594.89; Σxy = 275.8 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) X= y = b= ŷ= (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y y 22 20 18 16 14 12 10 0 y 22 20 14.4 18 y 22 VX 20 18 16 14 12 10 5 1 (c) Find the sample correlation coefficient r and the coefficient of determination 2. (Round your answers to three decimal places.) 16 14 12 5 2 3 4 19.9 14.4 19.6 20.0 1 1 2 2 3 3 4 4 5 22 6 20 18…
- Find E(R) and V (R) for a random variable R whose moment-generating function ismR(t) = e2t(1-3t2)-1Pv. Don't provide handwriting solution(d) Does a linear relation exist between the speed at which a ball is hit and the distance the ball travels? The variables speed at which the ball is hit and the distance the ball travels are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value ( ) (Round to three decimal places as needed.)
