Consider an MA(1) model and suppose we have the observed values Y₁ = 0, Y₂ = −1, and Y3 = 1/3. Find the conditional least squares estimator of 0 and the method of moments estimator of σ².
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.y y 90 54 50 53 80 91 35 41 60 48 35 61 60 71 40 56 60 71 55 68 40 47 65 36 55 53 35 11 50 68 60 70 65 57 90 79 50 79 35 59 A data set consist of dependent variable (y) and independent variable (x) as shown above. It is claims that the relationship between the x and y can be modelled through a regression model as follows: ŷ = a+bx where a and b are the estimated values for a and ß (refer to Appendix). (i) Determine the equation of the regression line to predict the y value from the x value. (ii) If the x value is 75, what is the value of y? (iii) Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of significance. (iv) Construct a 95% prediction interval for the y with x=35.Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply.
- For the regression model Yi = b0 + eI, derive the least squares estimator.Assume: qi= β0 + β1pi + ui Please derive the estimated values (b0 and b1) based on the equation using OLS (ordinary least squares regression). Show that they are unbiased estimators of β0 and β1.Consider the following. (-3,2) 1.5 (-1, 0) 0.5 (1,1) (a) Find the least squares regression line. y = (3,2) (b) Calculate S, the sum of the squared errors. Use the regression capabilities of a graphing utility to verify your results. S =
- The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y-hat = -0.0127 + 0.0180x The above equation implies that: each beer consumed increases blood alcohol by .0127 on average it takes 1.8 beers to increase blood alcohol content by .01 After consuming 1 beer, blood alcohol equals .0180. each beer consumed increases blood alcohol by 0.018Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 XA scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2 through the equation y = ae+Px2 8, where & is a random error that is always positive. Find a transformation of the data that will enable her to use a linear model to estimate B, and B,.
- The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y = -0.0127 + 0.0180x. Suppose that the legal limit to drive is a blood alcohol content of 0.08. If Ricky consumed 5 beers the model would predict that he would be:Find the least squares line y = ß1 + B2x that best fits the data points (0, 1), (2,0), (3, 1), (5, –1). What is the least squares error?tion 13 A least squares regression line a. may be used to predict a value of y if the corresponding value is given O b. implies a cause-effect relationship between x and y O c. can only be determined if a good linear relationship exists between x and y Od. All of these answers are correct.