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Write the model specification matrix for the model Par. =BotBix+ OnxitBox, based on a random sample of size 8.Write the model specification matrix for the model based on a random sample of size 10.2 Let C= - Let Y, and Y, be independent random variables with B[ Y ] = 3, E[Y,] = 9, and Var Y, = Var Y, = 16. (a) Find E[ C]. (b) Find E[CY], where Y = (c) Find Var Y. (d) Find Var CY.The three basic structural elements of a data processing system are files, flows, and processes. Files are collections of permanent records in the system, flows are data interfaces between the system and the environment, and processes are functionally defined logical manipulations of data. An investigation of the cost of developing software as related to files, flows, and processes was investigated. The following data are based on that study. Cost (in units of 1000) Files Flows Processes (v) (IJ) 22.6 44 15.0 33 15 78.1 80 80 28.0 24 21 80.5 50 24.5 18 20.5 41 13 147.6 187 137 4.2 19 15 48.2 50 21 20.5 48 17 Find a 95% confidence interval on Arx,, r, x, when x, = 12, x, = 40, and X, = 20.\fThe three basic structural elements of a data processing system are files, flows, and processes. Files are collections of permanent records in the system, flows are data interfaces between the system and the environment, and processes are functionally defined logical manipulations of data. An investigation of the cost of developing software as related to files, flows, and processes was investigated. The following data are based on that study. Cost (in units of 1000) Files Flows Processes ( v) 22.6 44 18 15.0 33 15 78.1 80 80 28.0 24 21 80.5 227 50 24.5 20 18 20.5 41 13 147.6 187 137 4.2 19 15 48.2 50 21 20.5 48 17 Find a 90% confidence interval on Ap.A study was conducted on the effect of water temperature and time in solution on the amount of dye absorbed by a certain kind of fabric. A standard amount of dye (200 milligrams/mg) was added to a fixed amount of water. The three temperature levels used in the experiment were 105, 120, and 135" C. The fabric was left in the water 15, 30, or 60 minutes (min). For each of these temperature-time combinations the amount of dye left inside the fabric was measured. The experiment yielded the following data: Dye in yarn (mg) Time in solution (min) Temperature of H,O(C) (v) ( x, ) 136 15 105 153 30 105 186 60 105 182 120 175 120 187 120 170 135 179 30 135 183 50 135 Estimate the curve of regression of Y on X1.A study was conducted on the effect of water temperature and time in solution on the amount of dye absorbed by a certain kind of fabric. A standard amount of dye (200 milligrams/mg) was added to a fixed amount of water. The three temperature levels used in the experiment were 105, 120, and 135' C. The fabric was left in the water 15, 30, or 60 minutes (min). For each of these temperature-time combinations the amount of dye left inside the fabric was measured. The experiment yielded the following data: Dye in yarn (mg) Time in solution (min) Temperature of H,O(C) (v) 136 15 105 153 30 105 186 105 182 120 175 120 187 120 170 135 179 135 183 60 135 If a dye solution is prepared with the temperature at 125: C and the fabric left in the solution for 20 min, how much dye, on the average, would you predict to be left in the fabric?A study on the burn time for the common Fourth of July sparkler was conducted. The variables considered were the length of the chemical coating that covers the tip of the sparkler (in inches) and the bum time (in seconds) of the sparkler. Seventeen sparklers were burned, and the values of the chemical coating (x) and the bum time ()) are given below. Ohs. no. Chemical length (in.) Burn time (sec.) 4.5 29 3.6 26 4.0 25 3.7 25 4.0 27 3.7 27 4.0 28 4.0 25 3.8 25 4.0 28 3.8 24 4.1 15 3.9 22 4.1 25 3.9 24 16 4.2 26 17 3.8 24 (a) Estimate the simple linear regression model with response variable burn time (y) and predictor variable chemical length (x). (b) Test for significant regression at o = 0.05. Is this a good model to predict burn time? (c) Can you think of other variables that should be included in a future study to improve prediction ability?A study was conducted on the effect of nitric acid dilutions on the accelerated weathering of wood. The acid pH levels of 2.0, 2.5, 3.0, 3.5, and 4.0 were tested with distilled water (pH 5.6) used as a control. An accelerated weathering chamber was used with times of 200, 400, 600, 800, and 1000 hours. Red cedar wafers of approximately 700 mp were obtained and weighed accurately for the start weight at the beginning of the experiment. At the end of the accelerated time, the wafers are again weighed for the final weight. The resulting data, including the difference in "start weight" and "final weight" are given in the following table. Obs no. PH Time Start wi. Final wi. Difference 2.0 200 693 669 24 2.01 400 696 647 40 2.0 700 621 2.0 800 692 601 91 2.0 1000 693 STS 18 2.5 200 697 617 20 2.5 400 698 656 42 2.5 600 698 632 66 2.5 693 612 86 2.5 1000 697 585 12 3.0 200 698 677 21 3.0 400 699 656 43 3.0 600 690 636 63 3.0 800 695 617 78 3.0 1000 598 597 101 3.5 2010 698 679 19 17 3.5 400 696 662 34 18 3.5 60O 698 641 ST 19 3.5 699 622 37 20 35 1000 698 598 100 21 4.0 200 695 677 18 22 4.0 400 661 37 23 4.0 GOD 604 543 51 24 4.0 BOD GOR 672 76 25 4.0 1000 700 602 26 5.6 201 695 677 5.6 400 695 662 28 5.6 600 642 56 29 5.6 800 698 625 73 30 5.6 1000 698 606 92 For the model you selected in Exercise 70, calculate RY, and test for significance at o = 0.05
