X; is a random a random sample from N(Hx 2) 1) Find MLE. Unbiased? Consistent? 2) Linear regression with constant of 1, compare with
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- ) In estimating the regression in the previous problem (#2), you are concerned that the t-statistics may be inflated because of serial correlation. You compute the DW statistic at 0.724 for the regression Based on the DW, what can you say about serial correlation between the residuals? Are they positively or negatively correlated? Or not correlated? Compute the sample correlation between the regression residuals from one period and those from the previous period. Perform a statistical test at the level to see if there is serial correlation. If you are using the table in the textbook, assume that the critical values of the DW statistic for 214 observations are about 0.11 higher than the critical values for 100 observations.Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?
- In estimating the regression in the previous problem (#2), you are concerned that the t-statistics may be inflated because of serial correlation. You compute the DW statistic at 0.724 for the regression. Compute the sample correlation between the regression residuals from one period and those from the previous period. Perform a statistical test at the level to see if there is serial correlation. If you are using the table in the textbook, assume that the critical values of the DW statistic for 214 observations are about 0.11 higher than the critical values for 100 observations.Given the residuals squared derived from the regression: Marks = ƒ(Study hours) Use the information from the following auxiliary regression (table attached) to conduct the Park test to detect for the presence of heteroscedasticity at a = 5%.A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.
- The data in Table 11.17 are given for 9 patients with aplastic anemia [11]. *11.1 Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). *11.2 Test for the statistical significance of this regression line using the F test. *11.3 What is R2 for the regression line in Problem 11.1?For the residuals derived from Sarah's regression, skewness (S) equals -0.93726 and kurtosis (K) equals 1.561158. Conduct the Jarque-Bera test of normality at α=0.01.Starting with the following null and alternative hypotheses:H0= Residuals are normally distributed.H1= Residuals are not normally distributed. part 3 Question 1 The JB test-statistic is given by ? Question 2 The χ2 statistic is given by?. Question 3 A. Since the JB statistic is greater than the χ2 statistic, H0 can be rejected. Therefore the alternative hypothesis is assumed. The residuals are not normally distributed. B. Since the JB statistic is greater than the χ2 statistic, H0 can be rejected. Therefore the null hypothesis is assumed. The residuals are normally distributed. C. Since the JB statistic is less than the χ2 statistic, H0 cannot be rejected. Therefore the null hypothesis is assumed. The residuals are normally distributed. D. Since the JB statistic is less…Jimmy tested a sample with of n=4 pairs of X and Y scores and found SSY = 48 and a Pearson correlation between X and Y of r = 0.4 Calculate whether the Fobserved in this regression experiment is significant at the ∞ = o.01 level
- Just parts d,e anf f of question 1 d) We conduct a simple regression of size on hhinc, now using robust standard errors. The regression output is reported in Table 2. Why are the estimated coefficients in Table 2 equal to the estimated coefficients in Table 1? Do the conclusions on the statistical significance at 5% of the coefficient of hhinc change between Tables 1 and 2? e) Now, using both the critical value and the p-value, test whether the coefficient of hhinc is statistically significant at 1%, by using the results in Table 1. Repeat the test by using the results in Table 2. Compare the results based on Table 1 with the results based on Table 2. Consider the results in Table 2. Compute the 99% confidence interval for hhinc. f) Consider the results in Table 2.How would you decide whether 0 is contained in the 99% confidence interval for the coefficient of hhinc, without actually computing the confidence interval?Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?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. Perform a t test for the significance of β1. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 > 0 Ha: β1 ≤ 0 b. H0: β1 ≠ 0 Ha: β1 = 0 c. H0: β1 < 0 Ha: β1 ≥ 0 d. H0: β1 = 0 Ha: β1 > 0 e. H0: β1 = 0 Ha: β1 ≠ 0 5. Find the value of the test statistic. (Round your answer to two decimal places.) 6. Find the p-value. (Round your answer to three decimal places.) p-value = 7. State your conclusion. a. Do not reject H0. There is sufficient evidence to conclude that β1 is significant. b. Reject H0. There is insufficient evidence to conclude that β1 is significant. c. Reject H0. There is sufficient evidence to conclude that β1 is significant. d. Do not reject H0. There is insufficient evidence to conclude that…
