22 From the following regression equations find the mean values of x and Y series. 8Y 10Y: 40X 18Y -66 214 %D
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- Using 30 time series observations, the regression Y= B1 + B2 X + B3 Z + u is estimated and some results are reported as the following;Y't = 2.04 + 0.25 Xt – 0.12 Ztse (0.86) (0.08) (0.17)and the estimated first order autocorrelation coefficient (rho) P'= 0.92a) Apply Durbin-Watson d Test if there exists 1st order autocorrelation problem in the errors at 5% level (Set your hypotheses)Using 30 time series observations, the regression Y= B1 + B2 X + B3 Z + u is estimated and some results are reported as the following; Y't = 2.04 + 0.25 Xt – 0.12 Ztse (0.86) (0.08) (0.17)and the estimated first order autocorrelation coefficient (rho) P'= 0.92a) Test if there exists 1st order autocorrelation problem in the errors at 5% level (Set your hypotheses)The following estimated regression equation based on 10 observations was presented. ŷ = 27.1870 + 0.5709x1 + 0.4920x2 Here, SST = 6,734.125, SSR = 6,213.375, sb1 = 0.0815, and sb2 = 0.0561 a. Compute MSR and MSE. (Round your answers to three decimal places.) b. Compute F and perform the appropriate F test and find p vaule. Use ? = 0.05. State the null and alternative hypotheses. state your conclusion c. Perform a t test for the significance of b1. Use a = 0.05. d. Perform a t test for the significance of b2. Use a = 0.05.
- The following estimated regression equation based on 10 observations was presented ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Compute MSR and MSE. (Round your answers to three decimal places.) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 ≠ 0 and β2 ≠ 0 Ha: One or more of the parameters is equal to zero. b. H0: β1 = β2 = 0 Ha: One or more of the parameters is not equal to zero. c. H0: β1 > β2 Ha: β1 ≤ β2 H0: β1 < β2 Ha: β1 ≥ β2 d. H0: β1 ≠ 0 and β2 = 0 Ha: β1 = 0 and β2 ≠ 0 2. Find the value of the test statistic. (Round your answer to two decimal places.) 3. Find the p-value. (Round your answer to three decimal places.) p-value = 4. State your conclusion. a. Reject H0. There is sufficient evidence to conclude that the overall model is significant. b. Do not reject H0. There…Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?If we let RX(t) = ln MX(t), show that R X(0) = μ and RX(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment-generating function MX(t) = e4(et−1)
- A CI is desired for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with ? = 2.2. (Round your answers to two decimal places.) (a) Compute a 95% CI for ? when n = 25 and x = 53.7. , watts(b) Compute a 95% CI for ? when n = 100 and x = 53.7. , watts(c) Compute a 99% CI for ? when n = 100 and x = 53.7. , watts(d) Compute an 82% CI for ? when n = 100 and x = 53.7. , watts(e) How large must n be if the width of the 99% interval for ? is to be 1.0? (Round your answer up to the nearest whole number.)n = You may need to use the appropriate table in the Appendix of Tables to answer this question.You conduct a regression of the squared residuals against the dummy variables X1, X2, and X3 and find that for the squared residuals regression: Multiple R 0.4145 R Square 0.1718 Adjusted R Square 0.1600 SEE 92.3760 Conduct a test at the level to see if conditional heteroskedasticity is present In view of your answer for a), what needs to be done?The following estimated regression equation is based on 30 observations. ŷ = 18.3 + 3.9x1 − 2.2x2 + 7.5x3 + 2.5x4 The values of SST and SSR are 1,805 and 1,762, respectively. a. Compute R2 = (to 3 decimals). b. Compute Ra2 = (to 3 decimals).
- Use the following linear regression equation to answer the questions. (d) x1 = 1.0 + 3.9x2 – 8.4x3 + 2.4x4 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 8 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.468. Construct a 90% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t critical ±Suppose we consider the following model: Xt2 = b0 + b1X2t-1 + ut The estimation of the model provided the following: Xt2 = 0.00043 + 0.23036X2t-1 t = (7.71) (4.97) R2 = 0.0531 d = 1.9933 where Xt2 is as defined before. Given a p value for b1 of .0001 what do conclude about the significance of the model?Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.