Question 1. Suppose that you run four restaurants. Let A be 0 and 1 for am and pm.Let B1, B2, B3 for dummy variables corresponding to restaurants labelled 1,2, and 3respectively. Let Y be 0 if no complaint is received and 1 otherwise.(a) [10 marks] Consider the logistic regression modellogit [P(Y - 1)] =-0.2-0.9A-1.3B₁-0.6B2-1.2B3 + 1.3AB₁ +0.7AB₂+ 0.3AB3Find the probability P(Y = 1) for each of the following cases.P(Y-1)ampmRestaurant 1Restaurant 2 Restaurant 3Restaurant 4(b) [10 marks] Consider the logistic regression modellogit[P(Y=1)]=-0.2-0.94-1.3B₁-0.6B2-1.2B3Find the probability P(Y - 1) for each of the following cases.P(Y-1)ampmRestaurant 1 Restaurant 2 Restaurant 3Restaurant 4

Imagine you're analyzing complaints at restaurants. Logistic regression can help predict the…

Answered: Question 1. Suppose that you run four…

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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(Medicare). The annual expenditures for Medicare (in billions of dollars) by the US Government for selected years since 1980 are shown in Table 4. Let x represent the years since 1980. (Use 4 decimal places in all answers.) Table 4: Medicare Expenditures Year Billion $ 1980 37 1985 72 1990 111 1995 181 2000 197 2005 330 A. Find the exponential regression model for the data.M(x) = B. What is the r2 value for this model?r2 = C. Extimate (to the nearest billion) the expenditures in 2008?The Medicare expenditures in 2008 were about $ billion.
Question: Give the equation of the model you chose in (b ) using the transformed variables .
Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y. Smoking status (S) equals 1 for at least one pack per day and 0 other- wise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. A. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fitted YS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable. B. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P -values refer to for…
Twenty members of an athletic club are studying the relationship between the time it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table. Term CoefCoef SE CoefSE Coef TT Constant 39.88 4.24 9.41 Time to fatigue 3.92 0.71 5.52 Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary = 10,815.11 +2563.46 (Education) +897.49(Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (8 years of education) and one has a master's degree ( 10 years of education). How much more money would we expect the employee with a master's degree to make? Answer Tables Keypac Keyboard Shortcu
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Can gender, educational level, and age predict the odds that someone votes for a particular candidate in the election? Over 1500 voters were selected, and data were col-lected on the highest year of school completed, their age, and their gender. We wish to t a logistic regression model: log(1 p p ) = 0 + 1Age + 2Education + 3Gender, where p is the binomial probability that a person voted for candidate Johnson, and gender is coded as the indicator for female. The R output is given below. parameter df estimate s.e z p-value (Intercept) 1 .1119 .3481 .321 .748 Age 1 .0020 .0032 .613 .54 Education 1 -.0100 .0184 .547 .585 Gender 1 .4282 .1040 4.117 .000 Null deviance: 255.95 on 1499 degrees of freedom Residual deviance: 220.80 on 1496 degrees of freedom Write down the tted logistic regression and give a short summary about the data analysis . Calculate the probability of voting for Johnson for a…
Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary = 10,896.07 + 2755.34 (Education) + 773.89 (Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (8.years of education) and one has a master's degree ( 10 years of education). How much more money would we expect the employee with a master's degree to make?
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
You decide to add a second independent variable to your regression. Male is a dummy variable that equals 1 if the individual is male and 0 otherwise. Your regression results are now: wage = 3.071 + 0.289 × Years of Schooling + 1.28 × Male (0.143) (0.0168) (0.624) Interpret the coefficients from this regression. Make sure to clearly indicate what is changing and what is constant in each interpretation. Determine whether each coefficient is statistically significant at each of the conventional significance levels. The R2 for this regression is 0.316. Interpret the meaning of this value.
Question 38. You have performed a linear regression analysis to explore sunflowers' growth (in meters per month) depending on the watering (in litres per day). You have estimated the regression coefficient to be ß = 1.6. What can you conclude? a) There is a signifleant correlation between watering and growth. b) An average sunflower growths 1.6 meters per month. c) If you give it an additional litre of water per day, there will be an additional average growth of 1.6 meters per month. d) According to the model assumptions, an additional litre of water per day will result in additional 19.2 meters of growth after one year. e) You should consider further influencing quantities.

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