Please answer 5.6 a-c, thanks! 5.5 For each of the following two time-series regression models, and assuming MR1-MR6 bolfind var(b, x) and examine whether the least squares estimator is consistent by checking whetherlim-var(b₂|x) = 0.a. y, =B₁ + B₂t+e,, t = 1,2,..., T. Note that x = (1, 2, ..., T), Σ(1-7)² = Σ₁²-2b. y, =B₁ + B₂ (0.5)' + e,,t = 1,2,..., T. Here, x = (0.5, 0.5²,...,0.5). Note that the sum of a geo= T(T+1)/2 and ₁² = T(T+1)(2T+1)/6.L=1to brusbrusmetric progression with first term r and common ratio risS=r+p²+³+...+² =r(1-r")1-rc. Provide an intuitive explanation for these results.5.6 Suppose that, from a sample of 63 observations, the least squares estimates and the correspondingestimated covariance matrix are given by3 -2 1]4 0cov (b₁,b₂, b3) = -21-1Using a 5% significance level, and an alternative hypothesis that the equality does not hold, test eachof the following null hypotheses:0 3 wollol adaa. B₂=0b. B₁+2B₂=5has moil tuquo smoc. B₁-B₂+ B3 = 45.7 After estimating the model y = B₁ + B₂x2 + 3x3 + e with N = 203 observations, we obtain the fol-lowing information: (2-₂)² = 1780.7, (3-3)² = 3453.3, b₂ = 0.7176, b3 = 1.0516,SSE=6800.0, and r23 = 0.7087.a. What are the standard errors of the least squares estimates b₂ and b3?b. Using a 5% significance level, test the hypothesis Ho:B₂ = 0 against the alternative H₁ : B₂ 0.c. Using a 10% significance level, test the hypothesis Ho:B3 ≤0.9 against the alternativeH₁:B₂>0.9.d. Given that cov (b₂, b3) = -0.019521, use a 1% significance level to test the hypothesis Ho: B₂ = ß3against the alternative H₁ :B₂ B3.5.8 There were 79 countries who competed in the 1996 Olympics and won at least oof these countries, let MEDALS be the total number of medals won, POPM be poFor eachillions,f.5.9 TC

As asked by you, I have answered question 5.6 a-c. Please find the explanation below. Thank you.

5.6 Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated covariance matrix are given by b₁ b₂ a. B₂=0 b. B₁ +28₂ = 5 c. B₁-B₂+ B₂ = 4 2 3 b₂ wollol ads nobizan QUAR 1X3101 tilbag Using a 5% significance level, and an alternative hypothesis that the equality does not hold, test each of the following null hypotheses: 3-2 1 cov (b₁,b₂, b3) = -2 4 0 1 0 3

5.6 Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated covariance matrix are given by b₁ b₂ a. B₂=0 b. B₁ +28₂ = 5 c. B₁-B₂+ B₂ = 4 2 3 b₂ wollol ads nobizan QUAR 1X3101 tilbag Using a 5% significance level, and an alternative hypothesis that the equality does not hold, test each of the following null hypotheses: 3-2 1 cov (b₁,b₂, b3) = -2 4 0 1 0 3

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 5EA

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 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 0.72, 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 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 16 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 45/62, 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 34000. From this information, what is the critical value needed to calculate the margin of error for a 95 percent confidence interval for one of the model coefficients? (a) 2.069 (b) 2.110 (c)…
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 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 0.8, 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 80000 and the sum of squared errors is (SSE) 20000. From this information, what is the value of the hypothesis test statistic for evidence that the true value of the coefficient of the second explanatory unknown exceeds 5? (a) 4 (b) 3…
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 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 model…
Suppose we perform a simple linear regression (SLR) of two variables F1 and F2 against the same out variable (say y). The r-squared value/score of both the SLRS are 0.9678 and 0.95123 respectively for F1 and F2. Then what can you say about the correlation? O a. y is more dependent on F2 than F1 O b. None of these O . The result does not say that y is more dependent on F1 OR F2 O d.y is more dependent on F1 than F2
Suppose Y; are the fitted y-values for in a maximum-likelihood linear regression model and Y; are the observed values, i = 1,2,... Show that E(Y: - Ý;) = 0 i=1
0. In a statistical study, it is found that variables z and y are correlated as follows. Find the least squares regression line in this model.
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2