1. !--- Which of the following assumptions is not needed for 3 to be an unbiased estimate of the population parameter 3 in the regression model y = a + B₁x₁ + B₂x₂ + U₁ where a is the intercept term, B is the slope parameter, and u is the unobserved error verm? A. The variance of the error term is homoskedastic, i.e. var (ulx₁, x₂) = 0². (B) The variable, x₁ and x2, are mean independent of the error term. E [ulx₁, x₂] = 0. C. No perfect collinearity D. We have a random sample of size n from the underlying population
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- A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…Consider the following regression equation specied for 2-period panel data: where i = 1; 2; :::N and t = 1; 2. If you expect that β_1 is positive, but the correlation between Δx_i and Δu_i is negative, thenwhat is the bias in the OLS estimator of β_1 in the first-differenced equation?Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance is
- 6. A real estate company wants to study the relationship between Home price in OMR 1000) and the following variables: Floor size (in 100 square feet) (x 1 ) , Type of Heating (X 2 =1 if electricity and X 2 =0 , if Gas), Location of home (X 3 =1 if in town and X 3 =0 , if in village). Use this to answer the following questions: Then the regression coefficient beta 2 is significant at 5% level. A. False B . None C. Not Enough evidence to make decision D. TrueWhich of the following statements is NOT true? a.If the correlation coefficent, rr, is negative, then the slope of the regression line must always be negative. b.For variables x and y, the value of the correlation coefficent will not change c.if the units of x and y are changed, (i.e., if both x and y are changed from say inches to meters) d.If r≠0r≠0 , then a significant linear correlation will exist between the two variables e.The value of the correlation coefficient must be within the interval: −1≤r≤1Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.
- A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…Assume that variables xx and yy have a significant correlation, and that the line of best fit has been calculated as ˆy=1.4x+3.6y^=1.4x+3.6. One observation is (9,16.3)(9,16.3).What is the predicted value of yy for the value x=9x=9? What is the residual for the value x=9x=9? What is the best interpretation for the residual? The value 16.316.3 is below the average value for yy when x=9x=9 The value 99 is above the average value for yy when y=16.3y=16.3 The value 16.316.3 is above the average value for yy when x=9x=9. The value 16.316.3 is below the average value for xx when y=16.32) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
- Suppose now that that Y denotes the annual salaries (in thousands of dollars) for US citizenswho are in their 40s and 50; and X is an indicator (dummy) variable: X = 1 if that workergraduated from college and X=0 otherwise. Suppose the average annual salary for this age groupis $45,000 and the estimate for β is β~ = 15 with s.e. = 5.a. What is the t-statistic and associated p-value for the null hypothesis that attending collegehas no impact on subsequent salary?b. What is the upper and lower bound of a 95-percent confidence interval for β~ ?c. In a credible research design attending college would be randomly assigned to a largesample of potential students. Propose such a research design. What are the potential ethicalissues?If the value of Cronbach’s alpha is 0.07, it means ___________; a. Research instrument is not reliable b. Research instrument is internally consistent c. Data is reliable d. Data is internally consistent1. 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 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.