Story In the east process, you believe that excessive variation in CBD content occurs during the cannabis oil extraction process. Several workers operate several different machines that convert cannabis plants into refined CBD oil. Those differences could affect the CBD levels. To learn more about this process, you conducted 2 experiments. In the first experiment, you processed 56 batches of oil in one machine for various lengths of time and at different ambient temperatures, and then measured the CBD content in grams. In the second experiment, you processed 56 batches of oil using various combinations of machines and workers, and then measured the CBD content in grams. Your goal is to find the "best" combination of time, temperature, and machine. The workers will then use this information to create their standard work instructions. Your main priority is to maximize the CBD content. Your secondary priority is to make the process more robust, so that a small mistake in setting the time or temperature would only slightly decrease the yield. Questions 1. Use linear regression to analyze the relationship that processing time and ambient temperature might have with CBD content in the first 56 batches of oil. In Excel, you can do this via the "Data - Data Analysis - Regression" feature; select the "Line Fit Plot", "Residual Plot", and "Normal Probability Plot" options. In SPSS, you can use the "Regression - Linear" feature. a) Include the regression results table in your assignment. You will need to adjust the table's format to make it more readable. b) For each explanatory variable, briefly interpret the coefficient B and its significance p. Also interpret the R of the overall model. What does each of these values indicate? c) Include 5 plots in your assignment as follows. You will need to adjust their formatting. 1. The line fit plot relative to time. Ensure that there are only 2 sets of data: the actual measurements should be represented by dots (with no line), and the predicted measurements should be represented by a line (with no dots). 2. The line fit plot relative to temperature. Ensure that there are only 2 sets of data: the actual measurements should be represented by dots (with no line), and the predicted measurements should be represented by a line (with no dots). (This will be messy.) 3. The residual plot relative to time. Do not include a line. 4. The residual plot relative to temperature. Do not include a line. 5. The normal probability plot. A line is optional. d) Briefly interpret these plots; your answer should be about 1 sentence per plot. Is linear regression reasonable for this data? (Report any problems you see, but do not fix them.) 2. Use two-factor ANOVA to investigate the relationships that worker and extraction machine type might have with CBD content for the 56 batches of oil. In Excel, you can do this via the "Data Data Analysis ANOVA: Two factor with replication" feature after you re-arrange the data on the spreadsheet. Or you can use the equivalent feature in SPSS. a) Include the ANOVA results table in your assignment; do not include the large data summary above it that Excel also produces. You will need to adjust the formatting to make the table more readable. b) Briefly interpret the ANOVA table's three p values. Which relationships were statistically significant and which ones were not? c) Create an interaction plot that displays the average CBD yield for each combination of machine and operator. (It should display either 2 or 4 lines.) d) Which combination of worker and machine had the highest yield? e) Describe the design of this experiment: What was the response? What were the factors and how many levels did each one have? How many treatment combinations were there? How many groups, replications, and runs were used? 7 Time 2 CBD yield at the east site 3 4 For Regression 5 Yield versus Time & Temperature 6 Minutes Degrees C grams Temperatu CBD For ANOVA Yield vs Machine & Operator grams Machine Operator CBD 8 30 20.5 4.21 CO2 Alex 81.71 9 35 21.7 10.20 CO2 Chris 79.14 10 40 23.1 13.07 CO2 Farah 78.37 11 45 19.5 26.23 CO2 Min 77.57 12 50 20.7 35.39 Ethanol Alex 82.53 13 55 22.7 46.29 Ethanol Chris 81.45 14 60 21.0 54.03 Ethanol Farah 86.08 15 65 21.8 65.46 Ethanol Min 86.76 16 70 22.3 77.64 CO2 Alex 81.38 17 75 19.5 79.51 CO2 Chris 82.99 18 80 21.9 79.72 CO2 Farah 81.67 19 85 22.7 80.93 CO2 Min 80.13 20 90 21.7 83.13 Ethanol Alex 81.54 21 95 23.0 83.56 Ethanol Chris 82.04 22 30 22.1 9.23 Ethanol Farah 86.26 23 35 20.1 6.06 Ethanol Min 89.33 24 40 21.3 17.58 CO2 Alex 82.40 25 45 22.2 28.25 CO2 Chris 81.01 26 50 21.9 37.53 CO2 Farah 79.41 27 55 21.3 49.34 CO2 Min 76.40 28 60 22.5 60.31 Ethanol Alex 85.09 29 65 19.7 65.60 Ethanol Chris 84.42 30 70 21.8 72.79 Ethanol Farah 85.88 31 75 22.9 75.65 Ethanol Min 88.85 32 80 21.7 75.05 CO2 Alex 85.82 33 85 22.5 75.71 CO2 Chris 80.17 34 90 23.3 79.76 CO2 Farah 78.97 35 95 20.6 86.37 CO2 Min 76.07 36 30 20.9 6.79 Ethanol Alex 85.37 37 35 22.8 2.13 Ethanol Chris 84.41 38 40 20.2 16.56 Ethanol Farah 87.91 39 45 21.4 25.65 Ethanol Mini 83.66 40 50 23.5 36.26 CO2 Alex 84.81 41 55 19.8 49.49 CO2 Chris 82.65 42 60 21.3 50.64 CO2 Farah 83.30 43 65 21.4 70.34 CO2 Min 78.76 44 70 20.3 74.15 Ethanol Alex 82.98 45 75 21.1 76.62 Ethanol Chris 84.99 46 80 23.8 80.06 Ethanol Farah 84.51 47 85 20.1 86.07 Ethanol Mini 84.44 48 90 21.3 85.68 CO2 Alex 82.40 49 95 21.7 77.98 CO2 Chris 80.68 50 30 21.2 4.63 CO2 Farah 77.55 51 35 22.4 9.16 CO2 Min 77.34 52 40 23.3 15.41 Ethanol Alex 82.09 53 45 19.2 23.17 Ethanol Chris 87.11 54 50 21.5 37.26 Ethanol Farah 86.36 55 55 22.3 48.41 Ethanol Mini 90.88 56 60 21.0 54.69 CO2 Alex 82.73 57 65 22.0 64.79 CO2 Chris 82.28 58 70 23.2 74.65 CO2 Farah 80.85 59 75 20.8 81.69 CO2 Min 77.28 60 80 21.6 80.49 Ethanol Alex 82.27 61 85 21.8 85.49 Ethanol Chris 84.97 62 90 19.2 81.77 Ethanol Farah 85.56 63 95 21.5 78.82 Ethanol Min 86.09 64