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- Suppose you have a joint distribution of x and y where • x has population mean ug and population variance o? • y has population mean ly and population variance o, and the population covariance between them is Ery. The population Pearson correlation is then given by Ery OxJy We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 (x; – Ha)(yi – µy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not. (b) Suppose we estimate our correlation with (xi – Ha)(Yi – Hy) - n i=1 Ox0y Is this an unbiased estimator of the population correlation? Show why or why not. =WI4. In a Exponential distribution with a λ of 5 defects per one square yard, the probability of finding a result less than 6 defects is almost 1 (100%).7. A company wanted to assess the impact of R and D expenditure (x) on annual profit (v) following table presents data for past 8 years. X: 7 5 10 4 5 3 y: 45 42 41 60 30 34 25 Compute the correlation co-efficient. Comment on the value. 20
- .A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.13. A standard logistic regression models the effect of age (20-29, 30-39, 40-49, 50-59, 60- 69) on experience of back pain (modeling yes vs. no). If age is included as a continuous covariate (with values 1, 2, 3, etc., as scores) and the regression parameter associated with age is estimated to be 0.21 with standard error of 0.08, what are the odds of backpain for a 35-year-old (e.g., in the 30-39 range) relative to the odds for a 25-year-old? Enter your answer to two numbers after the decimal place.1. The data are weekly averages of fasting blood glucose levels (m mols) of a diabetic patient treated with different doses of insulin (units) given over a period of 32 weeks. To recognize the trend in blood glucose change, 8 weeks from the treatment duration of first 12 weeks were chosen randomly and the data are as follows: Week 4 12 7 6 9 2 11 8 Blood sugar (m/mol): 8.1 4.0 5.3 6.1 5.7 7.3 4.8 4.6 Dose/day (units): 15 55 45 30 35 25 Lost 50 Evaluate the relationships between blood sugar levels and the dose of insulin/day. Describe and interpret this relationship?
- 2. Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature x (° F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y= 5 - 0.01x and the standard deviation o=0.075. a. What is the expected reaction time when temperature is 250° F? b. Suppose that five observations are made independently on reaction time, each one for a temperature of 250° F. What is the probability that all five times are between 2.4 and 2.6 hours?1. It has been noted that there is a positive correlation between the U.S. economy and the height of women's hemlines (distance from the floor of the bottom of a skirt or dress) with shorter skirts corresponding to economic growth and lower hemlines to periods of economic recession. Comment on the conclusion that economic factors cause hemlines to rise and fall. # of Absences (in weeks) Exam Grade 1 2 345 23 014 90 85 95 92 80Answer #2
- What is indicated by a Pearson correlation of r = +1.00 between X and Y? Question 1 options: Each time X increases, there is a perfectly predictable increase in Y Every change in X causes a change in Y Every increase in X causes an increase in Y All of the other 3 choices occur with a correlation of +1.00.llustration 19.18.. A sample study of the population of two districts gives that in district A the percentage of male population is 52% while this is the figure for the female percentage in the B district. If the size of the sample selected was in district A and B as 400 and 625 respectively, can both of these samples be taken to come from a population where the percentage of males and females is equal?. Find out the coefficient of correlation between the sales and expenses of the following 10 firms (figure in '000 Rs.) Firms: 1 3 4 6. 8. 9. 10 Sales: 50 50 55 60 65 65 65 60 60 50 Expenses: 11 13 14 16 16 15 15 14 13 13 Solution a.L