A GLM is fitted to independent binary observations {y} using the log link,log(i) = xẞ, i=1, n,where Ti=E(y) denotes the probability of success, xiXip) is avector of predictors and ß = (B₁, ß₁, ..., ß₂)² is a vector of unknown parameters=(xio, Xi1, (b) Write down the log-likelihood of ẞ and show that the (j, k) element of theexpected information matrix is given bynΠί-Xijxik(1 — πi)i=1(You should derive from scratch. Do not quote any results from the lecturenotes.)

Concept Explanation:- The problem is about a Generalized Linear Model (GLM) applied to binary data…

Answered: A GLM is fitted to independent binary…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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Suppose a logistic regression model is fitted for the probability of car ownership for residents of a certain city in Oman (Y=1 if a resident owns a car, Y=0 if a resident does not own a car). Suppose the explanatory variables used are x1=no. of years a resident spent in schooling and x2 is gender of the resident of the city (x2=1 for a male and x2=0 for a female resident) a) Interpret el and e82 b) if BO= -1.6, B1=0.4 and B2=3, estimate the probability of a resident in the city owning a car.
The equations of the regression line between two variables are expressed as 2x-3y=0 and 4y-5x-7=0 a) identify which of two can be called regression line of Y on X and X on Y b) find the correlation coefficient c) find mean value of X and mean value of Y
Use the formula to calculate the linear correlation coefficient for data with the following summary statistics:
Find the new data point (x,y) in which x=2 from the data points (1,3) and (4,12)
A study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ACBG = y, summary values are n = 26, Ex, = 1615, E(x, - x) = 3756.96, Ey, = 281.9, E(y, - v) = 465.34, and Exy, = 16,720. (a) Compute a 90% CI for the true correlation coefficient p. (Round your answers to four decimal places.) (b) Test H: p = -0.5 versus H: p < -0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. There is evidence that p < -0.5. O Fail to reject Ho: There is evidence that p < -0.5. O Fail to reject H. There is no evidence that p < -0.5. O Reject H.. There is no evidence that p < -0.5. (c) In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by…
You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: = 71.0 – 4.84×BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) Values in parenthesis are standard errors. (a) What is the interpretation of the intercept? What is the interpretation of the coefficient of the dummy variable? How tall are females, on average? (b) Test the hypothesis that females, on average, are shorter than males, at the 1% significance level.
A linear regression to quantify the salaries of the employees in a company is estimated, using the following variables: Y: the salary of the employee in 1000 SEK. Age: the age of the employee in years R: the categorical variable Education with 3 groups; Primary, Secondary, University. a)Write down a linear model with intercept for the variable Y based on Age and R, in which the Primary level of education is the reference category for the Education variable. b)Mention a test to see if the variable Age significantly improves the model fit?
The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y) 6.12 −0.088.01 0.25 8.57 −0.1410.61 0.00 12.5 0.08 11.94 0.03 12.55 −0.0717.93 0.29 18.24 0.23 19.84 0.24 20.3 0.19 19.12 0.14 17.78 0.05 19.57…
The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y) 6.22 −0.08 8.01 0.25 8.67 −0.14 10.61 0.00 12.5 0.08 11.94 0.03 12.55 −0.07 17.93 0.29 18.34 0.23…
The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. y 0.3 0.2 Mean Temperature (x) 0.1 0.0 -0.1 6.22 8.01 5 8.67 10.61 12.5 11.94 12.55 18.03 18.24 (a) Construct a scatterplot of the data. 19.94 20.3 19.02 17.78 19.67 USE SALT Net…
The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y) 6.12 −0.088.11 0.25 8.57 −0.1410.51 0.00 12.5 0.08 12.04 0.03 12.45 −0.0717.93 0.29 18.34 0.23 19.84 0.24 20.3 0.19 19.02 0.14 17.78 0.05 19.67…
What happens if the dependent variables are not correlated with each other? Will you still be able to perform MANOVA/MANCOVA?

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