More detail pleas see the file ,total have 8 questions; Now consider a multiple linear regression where the average length of stay in a hospital (Y) is anticipated to be related to infection risk (X1), routine chest X-ray ratio (X2), and available facilities and services (X3).1. (10) Use R to obtain the residual information on the MLR model Y~X1+X2+X3, check assumptions from the residual plot, BF test (you could do a grouping on Y) and Normality test.2.(5) For the MLR model Y~X1+X2+X3, use R to construct the design matrix X and Y, then compute the variance-covariance matrix of the residuals , what is the dimension of the matrix?3. (5) For the MLR model Y~X1+X2+X3, use R to construct the matrix X and Y, then compute the variance-covariance matrix of the parameter estimates , what is the dimension of the matrix? What are the standard error of the parameter estimates?4. (8) Obtain an interval estimate of the mean response when X1=4, X2=81, and X3=43 with 90% confidence level.Specify what are the point estimate, critical value, and the standard error.5. (4) Now consider the interval estimate of the single responsewhen X1=4, X2=81, and X3=43 with 90% confidence level. Without computation, discuss how the point estimate, critical value, and the standard error different are different from question 4.

Quantitative Math in Health ServicesCase Study 1: Forecasting Using the Northern College Health Services visit volume in Appendix 6-1 on page 113 of the textbook, for this assignment, you will be providing a forecast of the number of clinic visits for November 2008 using the average change, confidence interval, average percent change, moving averages, and exponential smoothing forecasting methods. Use the Internet or Strayer Library to research at least two (2) examples of the forecasting methods being used in health services organizations. Write a two to three (2-3) page paper in which you: Explain each step in the forecasting process for each method.Provide a brief summary of your researched health services organizations implementing the forecasting methods.Provide a forecast of the number of clinic visits for November 2008 using each method of the forecasting process.Conclude which forecasting method provides the best forecast, and provide a rationale for your conclusion. Your assignment must follow these formatting requirements: Be typed, double-spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions.Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length. The specific course learning outcomes associated with this assignment are: Evaluate forecasting strategies and methods.Use technology and information resources to research issues in quantitative methods for health services.Write clearly and concisely about quantitative methods for health services using proper writing mechanics. Grading for this assignment will be based on answer quality, logic / organization of the paper, and language and writing skills, using the following rubric. Case Study 1: Forecasting Criteria Unacceptable Below 70% F Fair 70-79% C Proficient 80-89% B Exemplary 90-100% A 1. Explain each step in the forecasting process for each method. Weight: 25% Did not submit or incompletely explained each step in the forecasting process for each method. Partially explained each step in the forecasting process for each method. Satisfactorily explained each step in the forecasting process for each method. Thoroughly explained each step in the forecasting process for each method. 2. Provide a brief summary of your researched health services organizations implementing the forecasting methods. Weight: 20% Did not submit or incompletely provided a brief summary of your researched health services organizations implementing the forecasting methods. Partially provided a brief summary of your researched health services organizations implementing the forecasting methods. Satisfactorily provided a brief summary of your researched health services organizations implementing the forecasting methods. Thoroughly provided a brief summary of your researched health services organizations implementing the forecasting methods. 3. Provide a forecast of the number of clinic visits for November 2008 using each method of the forecasting process. Weight: 25% Did not submit or incompletely provided a forecast of the number of clinic visits for November 2008 using each method of the forecasting process. Partially provided a forecast of the number of clinic visits for November 2008 using each method of the forecasting process. Satisfactorily provided a forecast of the number of clinic visits for November 2008 using each method of the forecasting process. Thoroughly provided a forecast of the number of clinic visits for November 2008 using each method of the forecasting process. 4. Conclude which forecasting method provides the best forecast, and provide a rationale for your conclusion. Weight: 15% Did not submit or incompletely concluded which forecasting method provides the best forecast; did not submit or incompletely provided a rationale for your conclusion. Partially concluded which forecasting method provides the best forecast; partially provided a rationale for your conclusion. Satisfactorily concluded which forecasting method provides the best forecast; satisfactorily provided a rationale for your conclusion. Thoroughly concluded which forecasting method provides the best forecast; thoroughly provided a rationale for your conclusion. 5. Writing / Support for ideas Weight: 5% Rarely uses reasons and evidence that logically support ideas. Partially uses reasons and evidence that logically support ideas. Mostly uses reasons and evidence that logically support ideas. Consistently uses reasons and evidence that logically support ideas. 6. Writing / Grammar and mechanics Weight: 5% Numerous errors in grammar, spelling, and punctuation. Partially free of errors in grammar, spelling, and punctuation. Mostly free of errors in grammar, spelling, and punctuation. Completely free of errors in grammar, spelling, and punctuation. 7. Writing / Documentation of research and sources Weight: 5% Insufficient or incorrect documentation of sources. Partly correct usage of in-text citations and references to document sources. Mostly correct usage of in-text citations and references to document sources. Completely correct usage of in-text citations and references to document sources.

Here is a list of the problems. Answers need to be provided in the attached Word document. 1.The singular form of the word “dice” is “die”. Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What’s the probability of getting a three at the third time? 2.There are 30 table tennis balls in the box: 6 are green, 10 are red, and 14 are yellow. If you shake the box and then randomly select one ball from the box, what’s the probability that you will get a red one: 3. Rachel was flipping a coin with Jerry. She told jerry: “I am able to get all heads in two tosses.” Jerry laughed at her: “No, the probability of getting two heads at two tosses is only__” 4. Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would receive the free tickets. What’s the probability of Jennie and Alex both getting free tickets? 5.Laura and Melissa were playing dice. What the probability of Laura and Melissa both getting a 6? 6. In a statistics class with 36 students, the professor wanted to know the probability that at least two students share the same birthday. The probability will be___ a. 0.1 b. Much smaller than 0.1 c. Much bigger than 0.1 d. Not possible 7. If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? 8. Jerry got a box full of colorful candy balls. There were 50 of them: 20 red, 10 green, 12 yellow and 8 blue. After shaking the box, he randomly selected 2 candy balls from the box. What’s the probability that the first one was blue and the second one was yellow? 9.Jerry got a box full of colorful candy balls. There were 50 of them: 20 red, 10 green, 12 yellow and 8 blue. After shaking the box, he randomly selected 2 candy balls from the box. What’s the probability that the first is blue and the second one is also blue? 10. Which activity could probabilities be computed using a Binomial Distribution? a. Flipping a coin a 100 times b. Throwing a die one hundred times c. The probability of getting a heart while playing card games d. Grades earned by 100 students on a statistics final exam 11. Many researchers have argued that the TB skin test is not accurate. Imagine that the TB skin test is only 70% accurate. Sarah is thinking about having the test. Before she has the test she wonders the probability that she has TB. The probability of Sarah having TB is … a. 70% b. 35% c. 30% d. More information needed to calculate 12. Imagine that the diabetic test accurately indicates the disease in 95% of the people who have it. What’s the miss rate? 13. Which of the following is the probability that subjects do not have the disease, but the test result is positive? a. Miss rate b. False positive rate c. Base rate d. Disease rate 14. In a normal distribution, the median is ____it’s mean and mode. a. Approximately equal to b. Bigger than c. Smaller than d. Unrelated to 15. In a normal distribution, __ percentage of the area under the curve is within one standard deviations of the mean? a. 68% b. 100% c. 95% d. It depends on the values of the mean and standard deviation 16. A normal distribution with a mean of 15 and standard deviation of 5. 95% of its area is within__ a. One standard deviation of the mean b. Two standard deviations of the mean c. Three standard deviations of the mean d. It depends on the value of the mode 17.The mean of a standard normal distribution is: a. 0 b. 1.0 c. -1.0 d. 100 18. The standard deviation of the mean for a standard distribution is: a. 0.0 b. 1.0 c. 100 d. 68% 19. A normal distribution with a mean of 25 and standard deviation of 5. What is the corresponding Z score for a case having a value of 10? 20. Consider a normal distribution with a mean of 25 and standard deviation of 4. Approximately, what proportion of the area lies between values of 17 and 33. a. 95% b. 68% c. 99% d. 50% 21. Consider a normal distribution with a mean of 10 and standard deviation of 25. What’s the Z score for the value of 35? 22. For a standard normal distribution, what’s the probability of getting a positive number? a. 50% b. 95% c. 68% d. We cannot tell from the given information 23.Two-hundred students took a statistics class. Their professor creatively decided to give each of them their Z-score instead of their grade. Rachel got her Z-score of -0.2. She was wondering how well she did on the exam. a. It was very good, much better than almost all of the other students b. It was so-so, but still better than half of the students. c. It was not that good, but not at the bottom of the distribution d. It was very bad and she needs to work much harder next time 24. A researcher collected some data and they form a normal distribution with a mean of zero. What’s the probability of getting a positive number from this distribution? a. 25% b. 50% c. 75% d. We need to calculate the standard deviation and then decide. 25. Which of the following description of distribution is correct? a. A Binomial distribution is a probability distribution for independent events for which there are only two possible outcomes b. You cannot use the normal distribution to approximate the binomial distribution c. Normal distributions cannot differ in their means and in their standard deviations. d. Standard normal distributions can differ in their means and in their standard deviations. 26. A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation? 27. Imagine you have a population of 100,000 cases. For which of the following degrees of freedom is the closest estimation of the population parameter? a. 4 b. 6 c. 10 d. 1000 28.Imagine that the average weight of a total of 500 girls in a high school is 35kg. Tom randomly sampled 10 girls and measured their weight. And then he repeated this procedure for three times. The means and standard deviations are listed as following. Which sample estimate shows the least sample variability? a. Sample one: mean=34, SE=5 b. Sample two: mean=30, SE=2 c. Sample three: mean= 26, SE=3 d. Sample four: mean= 38, SE=5 29. For which of the following degrees of freedom is a t distribution closest to a normal distribution? a. 10 b. 20 c. 5 d. 1000 30. In order to construct a confidence interval for the difference between two means, we are going to assume which of the followings? (Select all that apply) a. The two populations have the same variance. b. The populations are normally distributed. c. Each value is sampled independently from each other value. d. The two populations have similar means 31. A researcher tries to compare grades earned on the first quiz by boys and girls. He randomly chooses 10 students from boys and 15 students from girls and calculates the confidence interval on difference between means. How many degrees of freedom will you get in this t distribution? 32. Which of the following choices is not the possible confidence interval on the population values of a Pearson’s correlation? a. (0.3, 0.5) b. (-0.7, 0.9) c. (-1.2, 0.3) d. (0.6, 0.8)33. Which of the following descriptions of the t distribution is correct? (Select all that apply) a. With smaller sample sizes, the t distribution is leptokurtic b. When the sample size is large (more than 100), the t distribution is very similar to the standard normal distribution c. With larger sample sizes, the t distribution is leptokurtic d. The t distribution will never be close to normal distribution 34. _________________refers to whether or not an estimator tends to overestimate or underestimate a parameter. ______________ is the standard deviation of the sampling distribution and play a critical role in the constructing confidence intervals and in significance testing.a. Bias; standard error b. Sample population; Bias c. Mean; standard deviation d. Standard deviation; Mean 35. Which of the following descriptions of confidence intervals is correct? a. Confidence intervals can only be computed for the mean b. We can only use the normal distribution to compute confidence intervals c. Confidence intervals can be computed for various parameters d. Confidence intervals can only be computed for the population