Question 3 Provide brief, but complete, answers to the following questions. (i) (ii) Explain the properties of the regression line as chosen by the OLS method? Prove that Sum(e_i*Y-hat_i)=0 that is, the sum of the product of the residuals e_i and the estimated Y_i is always zero.
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- 2. Consider the following regression model and the result of estimation: distance Bo + B,angle + u %3D Where: distance = distance (in feet) traveled by a baseball, angle = the angle (in degrees) the baseball was hit, %3! u= regression error. Dependent Variable: DISTANCE Method: Least Squares Sample: 1 13 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob. C. ANGLE 32.93084 0.785542 5.146819 1.981191 0.0003 0.0731 169.4891 1.556309 a) Breusch-Godfrey test has been performed that produced the following result. Discuss the test result. Breusch-Godfrey Serial Correlation LM Test: Null hypothesis: No serial correlation at up to 2 lags F-statistic 6.534685 Prob. F(2,9) 7.698535 Prob. Chi-Square(2) 0.0177 0.0213 Obs R-squared b) RESET test has been performed that produced the following result. Discuss the test result. Ramsey RESET Test Equation: EQ01 Specification: DISTANCE C ANGLE Omitted Variables: Powers of fitted values from 2 to 3 Value 475.8260 60.71504 df…The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), x Well-Being Index Score, y 5 72 105 20 25 35 60 69.2 68.0 67.5 67.1 65.9 66.0 63.8 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. ŷ=x+ (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For every unit increase in commute time, the index score falls by (Round to three decimal places as needed.) OB. For every unit increase in index score, the commute time falls by (Round to three decimal places as needed.) 1 D. For an index score of zero, the commute time is predicted to be (Round to three decimal places as needed.) on average. on average. OC. For a commute time…XYZ Company's accountant is estimating next period's total overhead costs (Y). She performed three regression analyses, the first is based on direct labor hours (DLH), the second is based on machine hours (Mhr), and the third is based on quantity produced (Q). The results were: [Y=$95,000 + $9×DLH; R-square = 0.85]; [Y= $120,000 + $5xMhr; R-square = 0.15]; [Y=190,000+2Q; R-square=D0.45]. How much of the variations on the overhead costs is explained by the quantity produced (Q)? Select one: O a. 15% O b. None of the answers given C. 55% O d. 85% e. 45%
- Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit change x is prdicted toLuke used regression analysis to fit quadratic relations to monthly revenue, TR, and total cost, TC, data with the following results, where Q is quantity. TR = -0.008Q² + 32Q TC = 0.005Q² +2.2Q + 10 Given the computed amount Q in problem #2, its corresponding maximum profit is Blank 1 (round off to whole number).
- You estimated a linear regression model with 3 explanatory variables using a sample of 29 observations. You are asked to test the overall significance of the model.the F-statistics calculated is equal to 2.567 and the F-critical at 5% level is 3.028. The p-value of the test can be expressed as: Select one: O a. P(F(3,25)<=2.567) O b. 1-P(F(3,25)<=2.567) O c. P(F(3,25)<3.028) O d. 1-P(F(3,25)<33.28)A multiple regression analysis produced the following output from Minitab.Regression Analysis: Y versus x and xPredictor Coef SE Coef T PConstant -0.0626 0.2034 -0.31 0.762x 1.1003 0.5441 2.02 0.058x -0.8960 0.5548 -1.61 0.124S = 0.179449 R-Sq = 89.0% R-Sq(adj) = 87.8%Analysis of VarianceSource DF SS MS F PRegression 2 4.7013 2.3506 73.00 0.000ResidualError18 0.5796 0.0322Total 20 5.2809These results indicate that____________Consider a simple linear regression model, y = Bo + Bix+u.. What does the zero conditional mean assumption imply? The estimated average value of 31 is zero The expected value of the explained variable, y, is zero, regardless of what the value of the explanatory variable, x, is The expected value of the error term, u, is zero, regardless of what the value of the explanatory variable, x, is The estimated average value of 30 is zero
- When Y is regressed on X, B, > 0, sx+ 0, sy # 0, and the fraction of the variation in Y explained by the least-squares regression of Y on X does not equal 1. In this example, the sum of the squares of the deviations of the actual Y-values from their mean would definitely be greater than the sum of the squares of the deviations of the predicted Y-values from their mean. 1 A) B) true false 4. When Y is regressed on X, the sample slope is negative, sx + 0, sy + 0, and Y; = Y; for every observation. In this example, the sum of the squares of the deviations of the predicted Y-values from their mean would definitely be less than the sum of the squares of the deviations of the actual Y-values from their mean. A) В) true false 3.The standard deviation of the error terms in an estimated regression equation is known as:you are given the following model, where u and v are error terms meeting all standard assumptions of the linear regression: y= B1+B2 In(X2)+u y=B1+B2 Ln(X2)+ B3 X3+v One of the selection criteria between the 2 models is to choose the one with the highest R-Square Select one: O True O False