1.7. A study was conducted to analyse the effect of the size of the deposit level (X₂) and the likelihoodthat a returnable one-litre bottle will be returned. A return of a bottle recorded as Y = 1and noreturn Y = 0 was recorded.Use the following table to do a Pearson Chi-Square Goodness of Fit test in order to detect majordepartures from the logistic response function. That is that the logistic regression is a good fit forthe data.ft = [1 + exp(2.077 -0.136X]-¹Use x²(0.99, df) = 6.63 for a = 0.01, and determine the df-value.21030080ji | πιnjYjComplete the following table:123j=X₁41230050P₁ = Y/n Ojo not ret315300126E jo not retn - Ej1 retOj1 retChi Square22300150=Ej1 ret= n* πTotalsTotals Eo(Ojo - Ejo)²EjoTotals E₁(0₁₁ - Ej₁)²Ej₁

Given the table to do a Pearson Chi-Square of Fit test in order to detect major departures from the…

Answered: 1.7. A study was conducted to analyse…

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 survey was conducted and asked: "Do you consider your health to be poor?" This was coded as 1 for "yes" and 0 for "no." The effect of age (in years) and sex (1 male, 0 = female) on the outcome was examined using logistic regression. The fitted logistic model is: = logit(ô) = −0.544 + ß * sex + 0.0331 * age (a) What are the odds of responding "yes" for a female subject who is 60 years old? (b) What is the estimated odds ratio corresponding to the age variable? Interpret this estimate. (c) Suppose that, based on the data from the survey, the odds of responding "yes" for males are 3.79% greater than the odds for females, adjusting for age. What is the value of Â? (d) If we only wanted to assess the association between survey response (yes/no) and sex, what other method(s) (that we have learned in this class) could we have used (name at least one)? In your own words, explain why we cannot use the same method(s) if we want to consider the effects of both sex and age on survey response.
Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary = 11,433.70 + 3312.68(Education) + 819.54 (Experience ) Suppose an employee with 7 years of education has been with the company for 5 years (note that education years are the number of years after 8th grade). According to this model, what is his estimated annual salary? 囲 Tables E Keypad Answer Keyboard Shortcuts
If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. True or false?
9. A wildlife researcher is interested in predicting a mammal’s lifespan (in years) based on its average number of hours of sleep per night. Data was obtained from a large random sample of mammals, and the regression equation turned out as follows: Predicted lifespan = 36.93 – 1.64 (average hours of sleep) Which one of the following statements is a correct interpretation of this equation? 1. Approximately 1.64% of the variability in lifespan can be explained by the regression equation. 2. As lifespan increases by one year, average hours of sleep is predicted to decrease by 1.64 hours. 3. As lifespan increases by one year, average hours of sleep is predicted to increase by 36.93 hours. 4. As average hours of sleep increases by one hour, lifespan is predicted to increase by 36.93 years. 5. As average hours of sleep increases by one hour, lifespan is predicted to decrease by 1.64 years.
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…
q12
The following table shows both current and projected data on the number, in millions, of Facebook users in a certain country. t = years since 2012 F = number of Facebookusers (millions) 0 9.7 1 10.5 2 10.8 3 12.2 4 13.1 5 13.2 6 13.8 (a) Plot the data. (b) Find the equation of the regression line. (Round regression line parameters to two decimal places.) F(t) = Add the graph of the regression line to the plot from part (a). (c) Explain in practical terms the meaning of the slope of the regression line. (Round your answers to two decimal places). The slope of the regression line is million users per year. The slope means that, from 2012 on, the number of Facebook users in the country is expected to increase by million each year.
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…
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…
Question 5 5.1. A study was conducted to ascertain the effectiveness of a treatment of diseased plants. A recorded value of Y = 1 indicates that the treatment is effective and a value of Y = 0 is recorded when no effect is noticed. The outcome of the effectiveness of the treatment considers the treatment dosage, the above ground biomass, the rate of growth and the height of a plant recorded as 1 if above average height and recorded 0 as below average height. The following partial data set is provided. EFFECTS (Y) DOSAGE X₁ 0.2138 0.3907 0.2138 1 1 0 The output for running the full logistic regression model is given below: Coefficients (Intercept) HEIGHT BIOMASS RATE DOSAGE Estimate -1.23 0.31 0.33 0.34 -1.86 BIOMASS X₂ RATE X₂ 0.0525 1.1 0.0264 1.2 0.0920 1.3 Estimate -1.25 0.21 Std. Error 0.6795 0.6821 5.9374 2.4112 2.1420 Log Likelihood: -2.579 The output for the reduced model is given below: Coefficients (Intercept) BIOMASS Std. Error 0.4129 4.7390 6 z value -1.653 0.456 2.594 3.167…
The table below shows the average temperature in New York City (NYC), measured in degrees Fahrenheit (°F), where January is month 1, February is month 2, etc. Jul Jan 38.8 21.3 59.2 Using the regression, the average annual temperature in NYC is predicted to be 58.4 Jun Aug Oct Nov Feb Mar Apr 40.5 47.3 56.8 Sep 72.7 62.4 53.2 76.8 80.1 The data above can be modelled by an equation in the form y = a sin (bx+c) + d. 60.0 Ma 68.4 sin Dec 43.0
The data presented is a multiple logistic regression analysis and the models are shown below. In the models below, the data are coded as follows: p = the proportion of children with a diagnosis of ADHD, Child Exposed and Father’s Diagnosis are coded as 1 = yes and 0 = no. What is the odds ratio adjusted for father’s diagnosis? (Hint: Use only the appropriate model to find the odds ratio) (1) = –2.216 + 1.480 Child exposed (2) Father with diagnosis: = –1.665 + 1.297 Child exposed (3) Father without diagnosis: = –2.343 + 0.823 Child exposed (4) = –2.398 + 1.501 Child exposed + 0.906 Father’s diagnosis

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