Consider a simple linear regression model y = Bo + B1x + e. Clearly state the four basic assumptions about the general form of the probability distribution of e: Assumption 1: Assumption 2: Assumption 3: Assumption 4:

The following table shows the annual number of PhD graduates in a country in various fields.   NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =    What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate.   The slope tells us the decrease in the number of social science doctorates for each additional education doctorate.    The slope tells us the increase in the number of social science doctorates for each additional education doctorate.…

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…

Interpret the coefficient for tenure in terms of percentage change in odds of churning (tenure is calculated/recorded in years).

In a study investigating maternal risk factors for congenital syphilis, syphilis is treated as a binary outcome variable, where 1 represents the presence of disease in a newborn and 0 represents absence of disease. The estimated coefficients from a logistic regression model containing the predictors cocaine or crack use, marital status, number of prenatal visits to a doctor, alcohol use and level of education are included in the table below. The estimated intercept is not included in the table. a. As an expectant mother’s number of prenatal visits to the doctor increases, does the probability that her child will be born with congenital syphilis increase or decrease?b. Marital status is a binary variable, where 1 indicates that a woman is unmarried and 0 indicates that she is married. What are the estimated relative odds that a newborn will suffer from syphilis for unmarried versus married mothers after holding the other variables in the model constant?c. Cocaine or crack use is also a…

Indicate whether 25 is sufficient or whether a sample of 50 would be necessary. You will want to calculate the probability of the sample mean being between $11,000 and $13,000 for both a sample size of 25 and 50. (Thank You!)

3. Regression analysis breaks scores on the DV into... (explain and give equations)