In a simple linear regression based on 20 observations, it is found b1 = 3.05 and se(b1) = 1.30. Consider the hypothesis : H0 : β1 = 0 and HA : β1 ≠ 0 . Calculate the value of the test statistic.
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In a simple linear regression based on 20 observations, it is found b1 = 3.05 and se(b1) = 1.30. Consider the hypothesis : H0 : β1 = 0 and HA : β1 ≠ 0 . Calculate the value of the test statistic.
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- Consider the generalised linear regression model: y = Xẞ + e, with E[e] = 0 and E[ee] = 022. Let the model be estimated using both OLS and GLS, and let the OLS estimator of ẞ be denoted as BOLS and its GLS estimator as BGLS. Which of the following statements are incorrect about the OLS and GLS estimators? (a) BOLS is BLUE (b) BGLS is BLUE (c) The variance of BOLS cannot be less than that of BGLS (d) BGLS is more efficient that BOLSThe regression analysis is normally depicted as "y = Ax+ B." What does "A" indicate in the equation? A) It is the expected change in the independent variable for a one-unit change in the dependent variable OB) It is the significance level for the test OC) It is the expected change in the dependent variable for a one-unit change in the independent variable OD) The confidence intervalConsider the following time series: a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the forecast for t = 6?
- Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = 0.2, P(s2) = 0.5, and P(s3) = 0.3. With sample information I, P(I|s1) = 0.1, P(I|s2) = 0.05, and P(I|s3) = 0.2. Compute the revised (or posterior) probabilities: P(s1|I), P(s2|I), and P(s3|I).Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using a = .0901, z = O -1,96 O -1.86 O -1,34 O -1.645 O o o oConsider the following data for a dependent variable y and two independent variables, x1 and 12. 30 12 94 47 10 109 25 18 112 51 16 178 40 94 51 19 175 75 171 36 12 118 59 13 143 77 17 212 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating Y to ¤1. Predict y if æ1 = 35. b. Develop an estimated regression equation relating y to x2. ŷ = + Predict y if x2 = 25. ŷ = c. Develop an estimated regression equation relating y to ¤1 and 2. Predict y if x1 = 35 and x2 = 25. ŷ =
- In comparing two regression models that were developed using the same data, we might say that the model with the higher R2 value will provide the most accurate predictions. Is this true? Why or why not? If not, what would be the better parameter to use to compare two regression models? Provide at least one example to illustrate your arguments.The regression line in a scatterplot is also known as a(n): A. R-squared line. B. high-low line. C. outcome variable. D. linear trendline.(2 points) Suppose that we are to conduct the following hypothesis test: Ho p H₁ == 1050 1050 στ == Suppose that you also know that σ = 250, n = 95, 1090, and take a = 0.1. Draw the sampling distribution, and use it to determine each of the following: A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (-00, a) is expressed (-infty, a), an answer of the form (b, x) is expressed (b, infty), and an answer of the form (-00, a) U (b, c) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic: C. The p-value is D. Your decision for the hypothesis test: A. Do Not Reject H₁. B. Do Not Reject Ho- C. Reject Ho D. Reject H₁.
- Find the numerical value of factor (F/A,19%,20) using: a) the interpolation. b) the formula.Use the following information to answer the question. Based on above data, determine the expected return? Select one: a. 12.06% b. 19% c. 17.35% d. 16.72%In the linear regression equation y = a + bx, the letter b is best described as a (n):
