2. We wish to analyze the monthly water usage of a production plant, Y (in gallons), withrespect to its monthly production X₁ (in tons), mean monthly temperature X₂ (in °F)and the monthly number of days X3 of plant operation using the data given in the file'WATER.xlsx'. The following models are considered:I:II:Y =Y =Bo + B₁X₁ + B₂X2 + ß3X3 + E,Bo + B₁X₁ + B2X2 + B3X3 + B₁X1X2 + B5X₁X3 + B6X2X3 + εPerform your tests at a = 10% in this question.(a) Generate a matrix scatter plot and state the relationship among these variables.(b) Use R/Minitab to estimate the parameters of Model I, set up three hypotheses to testwhether each variable is useful given that the other variables are in the model.(c) In Model II, the interaction terms among these three variables are considered. Usingthe sum of squared residuals from the estimates of models I and II, do an F-test totest the whether all these interaction terms are useful jointly in predicting the monthlywater usage of the production plant.1(d) Use backward selection to perform the model selection based on Model II as the fullmodel.i. State your selected model. Is it a good model for the prediction of monthly waterusage of the production plant? Explain your answer.ii. Use your model in 2(d)i to estimate the water usage of the plant during a monthwhen its production is 90.0 tons, the mean temperature is 65 °F, and it operatesfor 20 days. ABWater Production2228260930885237861980717178 27239 203110 190211 1721123+412225413 252214260915222816255917 272318 308819 252220 201221225422 24362324624214725237826203127171728 211729 190230 225131 235732172133198098.5108.2109.610183.370144.784.497.4131.882.164.51089711314410964918212611185101847010797989613284DDays67.41970.32082.12169.22164.5 1963.7 2158 192017231844.1 19702068Temperature58.136.649.644.366588244614459621999903aa132120182121541869215820642151 22361756 2285 1949 2364 19

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • X2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables S 1 0 if not { if advanced 1 if aeroderivative X3 = and X4 if not If the engine type is traditional, then x3 = and x4 When you plug in these two values in the complete second-order model equation, you will get the model equation for traditional engine type.
The authors of the paper "Power-Load Prediction Based on Multiple Linear Regression Model"t were interested in predicting the load on the electric power system in China using data on y = Power consumption (in hundreds of millions of kwh), x, Population (in millions), and x, = Gross domestic %3D product (in billions of dollars), for 21 years. The model equation proposed in the paper is y = -113,527 + 0.974x, + 0.057x, + e. (a) According to this model, what is the mean power consumption (in hundreds of millions of kwh) for a year if the population was 160,000 million and the gross domestic product was 600,000 billion dollars? hundreds of millions of kwh (b) Interpret the value of B, in this model. When the [ gross domestic product v is fixed, the mean increase in [power consumption (in hundreds of millions of kwh) V associated with a 1-million unit increase in [population is 0.974.
2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231
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The line of best fit through a set of data is y=−40.623+2.293xyAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 40?y = Round to 1 decimal place.
Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 0.01x and a = 0.085. USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase hr hr 9°F increase (b) What is the expected reaction time when temperature is 220°F? When temperature is 260°F? 220°F hr ✓hr 260°F 2.5 (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.37 and 2.63 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.) 0.4602 X You…
Using the following table, I'm not sure how to answer these questions: a) Find the estimated regression equation of price on the percentage of space containing ads. y^ = +( )x b) Predict the price of a magazine with 47% of is space containing ads. rounding to 3 decimal places c) Estimate the price of a magazine with 98% of its space containing ads. Runded to 3 decimal places
Step 9 (d) What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? The proportion of the observed variation in efficiency ratio which can be attributed to the simple linear regression relationship is equal to the coefficient of determination, r². r² = 1- SSE SST' where SSE = Syy - B₁Sxy, and SST = Syy. First, use v² = 77.1001, (v₁)² = (40.17)² = 1,613.6289, and n = 24 to calculate Sy yy' Swy = y? - = 77.1001 n Since SST = S, 1,613.6289 24 Syy, it follows that SST = Submit Skip (you cannot come back) rounded to six decimal places.
The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the value of the slope (b) estimated in the linear prediction equation provided above (= 22-1.3x)? Also, interpret the slope. Estimated slope (b): Interpretation of slope:
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A chemical process was studied using a 2k design. Using ANOVA, the results have been modeled to produce the following linear equation in coded units: Vield =28.360+0.615 Temperature +0.485 Time Along the direction of steepest ascent. how many coded units must be moved in the Time direction for each step of one coded unit in the Temperature direction? Express your answer to 3 decimal places (XXXXX) Your Answer:
A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • x2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables S 1 {o if if advanced if aeroderivative and x4 X3 = not 0 if not Write a complete second-order model for heat rate (y ) as a function of cycle speed, cycle pressure ratio, and engine type.

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