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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Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
Assume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?
Two pumps capable of delivering 100 hp to an agricultural application are being evaluated in a present economy study. The selected pump will only be utilized for one year, and it will have no market value at the end of the year. Pertinent data are summarized as given follows. If electric power costs $0.10 per kWh and the pump will be operated 4,000 hours per year, which pump should be chosen? Recall that 1 hp = 0.746 kW.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.3 6.9 3.9 2.7 2.4 2.1 0.7 yy 14.3 11.3 10 7.4 6.5 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.Use the equation with the values rounded to two decimal places to make your predictions.A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer = Round to 3 decimal places.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.6 6.8 3.8 2.6 2.7 2.5 0.5 yy 14 11.5 9.6 7.2 5.9 6.5 6.3 4.6 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.08. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 7.8 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.5 thousand automatic weapons?Answer = Round to 3 decimal places.
In Step 2: Construct an estimated simple linear regression model how did you come up with the column X*X ?
A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40°C. Round the answers to three decimal places. The 95% prediction interval is ( , ).
A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Compute the error variance estimate s2. Round the answer to three decimal places.
Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?
A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.5x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.5 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find 95% confidence intervals for β0 and β1. Round the answers to three decimal places. The 95% confidence interval for β0 is ( , ). The 95% confidence interval for β1 is ( , ).
Consider the following variables: Y=daily productivity score (measured in points) X1=0 if undergraduate student,1 if graduate student X2=hours of sleep per night 1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test? A. Use Model 3 and test H0: β2=0 B. Use Model 5 and test H0: β3=0 C. Use Model 5 and test H0: β1=0 D. Use Model 5 and test H0: β2=0 E. Use Model 2 and test H0: β1=0 2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following: Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2) What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students? A. 2 B. None of…
Can somebody give me the rules on how to classify the equilibrium points?

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