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- The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Test the claim, at the α = 0.05 level of significance, that a linear relation exists between the two variables, Apply classical and traditional approaches. Show step1-step3.An article in Technometrics by S. C. Narula and J. F. Wellington ("Prediction, Linear Regression, and a Minimum Sum of Relative Errors," Vol. 19, 1977) presents data on the selling price (y) and annual taxes (x) for 24 houses. The taxes include local, school and county taxes. The data are shown in the following table. Sale Price/1000 Taxes/1000 25.9 4.9176 29.5 5.0208 27.9 4.5429 25.9 4.5573 29.9 5.0597 29.9 3.8910 30.9 5.8980 28.9 5.6039 35.9 5.8282 31.5 5.3003 31.0 6.2712 30.9 5.9592 30.0 5.0500 36.9 8.2464 41.9 6.6969 40.5 7.7841 43.9 9.0384 37.5 5.9894 37.9 7.5422 44.5 8.7951 37.9 6.0831 38.9 8.3607 36.9 8.1400 45.8 9.1416Define the concept of Weighted Least Squares?
- The residual plot shows the residuals for the least- squares line relating price of a used car (y) to the number of miles driven (x). Residuals Residual Plot for Miles Driven vs Price 10,000 5,000 -5,000 50,000 100,000 150,000 200,000 Number of Miles Driven Based on the residual plot, is the linear model appropriate for the relationship between miles and price? No, because there are clear outliers in the residual plot. No, because there is a clear curved pattern in the residual plot. No, because there does not appear to be a pattern to the residuals. Yes, because there is a clear curved pattern in the residual plot. Yes, because there does not appear to be a pattern to the residuals.Explain the Zero Conditional Mean Assumption and Generalized Least Squares?In the following table, price of a used car is given in terms of the percentage of the car's original price. Want to estimate price of a used car based on its mileage and age. Find the best linear fit to minimize the 2-norm of the approximation error. Age Mileage Percent of Original Price 1 5000 90 2 10000 85 2 15000 80 3 15000 75 34 20000 75 20000 70 4 30000 65 55 30000 60 40000 50
- In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25."ple: Find the linear least squares approximation to the data: - 1 0.5 Yi 2 4Explain why it can be dangerous to use the least-squares line to obtain predictions for x values that are substantially larger or smaller than those contained in the sample. The least-squares line is based on the x values ---Select--- ✓the sample. We do not know that the same linear relationship will apply for x values ---Select--- the range of values in the sample. Therefore the least-squares line should not be used for x values ---Select--- the range of values in the sample.
- National income from manufacturing industries is to be estimated for 1989 from a sample of 6 of the 19 industry categories that reported figures early for that year. Incomes from all 19 industries are known for 1980 and the total is $674 billion. From the data provided, estimate the total national income from manufacturing in 1989, with a bound on the error. All figures are in billions of constant (1982) dollars. Industry 1980 1989 Lumber and wood products Electrie and electronie 21 63 26 91 equipment Motor vehicles and 91 47 equipment Food and kindred products Textile mill products 70 70 60 70 Chemicals and allied 50 50 products a. Find a ratio estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. b. Find a regression estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. c. Find a difference estimator of the 1989 total income, and place a bound on the error of estimation. d. Which of…spss/minitabState whether the statement is true, false or uncertain and explain the answers chosen. (a). The ordinary least squares approach can be used to estimate the logit. (b). The problem of whether being a female has an effect on earnings could be analyzed using the probit and logit estimation. (C). The Akaike's information criterion is useful for only non nested models