Tutorial-10-Problems

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 1 if advanced 3o if not if aeroderivative 3o if not X3 = and x4 = Write the model equation for advanced engine type.

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 (1 if advanced X3 = 0 if not {o 1 and X4 = ここ if aeroderivative 0if not There are 67 observations in the dataset. We conduct a global F-test for overall model adequacy at a level of significance 5%. 1. Numerator degrees of freedom 2. Denominator degrees of freedom 3. If F-value equals to 30.52, then we (reject or fail to reject) the null hypothesis at 5%. There is (sufficient or insufficient) that the complete second-order model is overall useful.

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.

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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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

ECONOMETRICS:  Consider the information in the picture. Describe carefully how we could estimate this equation in First What does that mean and would it lead to consistent parameter estimates? Explain.

tion question Figure 2 shows the relationship in Africa between annual all-cause mortality rates in children ages 0-4 and P. falciparum malaria transmission intensity. Regions are classified into one of four categories based on childhood malaria prevalence: 1 childhood infection prevalence ranges from 0-24% 2-childhood infection prevalence ranges from 25-50% 3-childhood infection prevalence ranges from 51-74% 4-childhood infection prevalence ranges from 75-100% Annual mortality rate/1000 80 60 40 20 10 1 2 3 4 Intensity of P. falciparum transmission

Consider the AR(2) process Xt = 0.7 Xt-1-0.1 Xt-2 + Zt,

The flow rate y (m/min) in a device used for air-quality measurement depends on the pressure drop x (in. of water) across the device's filter. Suppose that for x values between 5 and 20, the two variables are related according to the simple linear regression model with true regression line y = -0.13 + 0.095x. n USE SALT (a) What is the expected change in flow rate associated with a 1 in. increase in pressure drop? (m3/min) Explain. O we expect the change in flow rate (x) to be the slope of the regression line. O we expect the change in flow rate (x) to be the y-intercept of the regression line. O We expect the change in flow rate (y) to be the slope of the regression line. O We expect the change in flow rate (y) to be the y-intercept of the regression line. (b) What change in flow rate can be expected when pressure drop decreases by 5 in.? (m³/min) (c) What is the expected flow rate for a pressure drop of 10 in.? A drop of 16 in.? 10 in. drop (m³/min) 16 in. drop | (m³/min) (d) Suppose…

Fitts' Law is a robust and highly adopted model of human movement. According to Fitts' Law, the time T required to move and select a target of width W that lies at a distance (or amplitude) A is T = a + b log2(2A/W) %D where a and b are constants estimated using simple linear regression. The quantity log,(2A/W) is termed the Index of Difficulty (ID) and represents the independent variable (measured in "bits") in the model. Research reported in the Special Interest Group on Computer-Human Interaction Bulletin (July 1993) used Fitts' Law to model the time (in milliseconds) required to perform a certain task on a computer. Based on data collected for n = 160 trials (using different values of A and W), the following least squares prediction equation was obtained: Î = 175.4 + 133.2(ID) %3D a. Interpret the estimates, 175.4 and 133.2. b. The coefficient of correlation for the analysis is r = .951. Interpret this value. c. Conduct a test to determine whether the model using Fitts' Law is…

The flow rate y (m³/min) in a device used for air-quality measurement depends on the pressure drop x (in. of water) across the device's filter. Suppose that for x values between 5 and 20, the two variables are related according to the simple linear regression model with true regression line y = -0.14 + 0.095x. n USE SALT (a) What is the expected change in flow rate associated with a 1 in. increase in pressure drop? |(m³/min) Explain. We expect the change in flow rate (x) to be the y-intercept of the regression line. We expect the change in flow rate (x) to be the slope of the regression line. We expect the change in flow rate (y) to be the slope of the regression line. We expect the change in flow rate (y) to be the y-intercept of the regression line. (b) What change in flow rate can be expected when pressure drop decreases by 5 in.? | (m³/min) (c) What is the expected flow rate for a pressure drop of 10 in.? A drop of 17 in.? 10 in. drop (m³/min) 17 in. drop | (m3/min) (d) Suppose o =…

1.Consider the following two simple regression models : Model I : Y, = B, + B,X, + µ; : Y, = a, +a, (X, - )+v, Model II (1) What is the estimator for B1? What is the estimator for a1? Are they the same to each other? Do they have the same variance? (2) What is the estimator for B2? What is the estimator for a2? Are they the same to each other? Do they have the same variance?

Starfish coildots is a disease affecting approximately 40 different species of sea stars and several other echinoderms. A sample of 240 ochre starfish and 155 sunflower starfish found that 97 ochre starfish and 54 sunflower starfish showed signs of infection. Is there evidence to suggest that the difference in the proportion of infected ochre starfish is greater than the proportion of infected sunflower starfish? (a) Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study. (b) Calculate the observed test statistic and state the distribution it follows (including degrees of freedom, if needed). (c) Give the p-value, or a range of appropriate values for the p-value. (d) Using the significance level α = 0.10, state your conclusions regarding the proportion of infected starfish in a plain English sentence. (e) Determine the 90% confidence interval for the difference in the proportions of infected ochre starfish and…

Suppose that you have the following three regression models: Yi B₁ + B₂x₁ + Uj regression) Y₁ = a₁ + a₂x₁ + eį, if i is male male individuals) Yi = ₁ + ₂x₁ + Ei, if i is female (separate regression for female individuals) ESS RSS The error terms satisfies that E[ui] = E[ei] = E[ei] = 0. Then, we find the following RSS and ESS: Pooled Regression 124.3 25 (separate regression for (pooled 71.1 11.4 separate separate regression for regression for male individuals female individuals 56.6 8.6 The number of sample size is given by 18. Select the correct statement(s). The RSS from the pooled regression is always smaller than the sum of RSSS from the separate regression models. In the above setup, Chow test is equal to 2. If e; is correlated with €;, then the OLS estimator of a2 from the separate regression will be is biased. If the variances of e; is different from €;, then the OLS estimator of 3₂ is no longer unbiased estimator. If we add another variable z; to the pooled regression, then the…

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A-4. Suppose the independent variable is X and the dependent variable is Y, what is the most appropriate regression equation for testing how a percentage increase in X influences the a percentage increase in Y? A. Ln(Y) = bo + bıln(X) B. Ln(Y) = bo + b1X C. Y = bo+biLn(X) D. Y = bo + bịX

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 = 4.10 - 0.01x and o = 0.07. n 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 g°F increase hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 260°F? 190°F hr 260°F hr (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 1.39 and 1.61 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.)

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…