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- Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
- The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.bex Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 3.136512 0.964065 0.985521 0.971252 0971252 Given the above regression statistics, what is the value of the coefficient of determination? 0.964065 3.136512Choose the correct option that best represents the pattern observed in the time-series graph. Ocean Waves 45 35- 30- 20- 154 10- V Time Series Plot of Ocean Waves 50 Index 60 70 The trend is increasing over time. The trend is decreasing over time. O The trend is relatively stable with no significant changes. The trend exhibits periodic fluctuations. None of the above are correct. 80 90 99 20.2
- Accountants at the Tucson firm, Larry Youdelman,CPAs, believed that several traveling executives were submittingunusually high travel vouchers when they returned from businesstrips. First, they took a sample of 200 vo uchers submitted fromthe past year. Then they developed the following multiple regressionequation relating expected travel cost to number of days onthe road (x1) and distance traveled (x2) in miles:y = $90.00 + $48.50x1 + $.40x2The coefficient of correlation computed was .68.a) If Barba ra Downey returns from a 300-miJe trip that took herout of town for 5 days, what is the expected amount she shouldclaim as expenses?b) Downey submitted a reimbursement request for $685. Whatshould the accountant do?c) Should any other variables be included? Which ones? Why?The mean annual earning for U.S. workers with advanced degrees is $80,977 with a standard deviation of $100,895; the distribution is highly right-skewed. Use this information to answer questions 7 to 10 below. A random sample of n = 86 workers is drawn, and their annual earnings recorded. What is the expected value of the sample mean of their annual earnings? What is the standard deviation of the sample mean of their annual earnings? what is the probability that the sample mean is at least $100,000? The actual sample mean earnings for the random sample of 86 workers with advanced degrees was $82,105. What is the sampling error?Explain the means and the use of variance and the Standard Deviation. Support your answer with example
- A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. (300 words) Table: Coefficients Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90 R2 = 0.67; DW = 2.08 Dependent Variable: House price (Pakistani rupees in Million) You are required to write the multiple regression How would you interpret the above ‘Output’ of a regression analysis performed in SPSS? From the above results, what can you say about the nature of autocorrelation? Is there multicollinearity in regression? How do you know?Emenyi Company Limited is considering using Markov analysis to analyze brand switching between three different brands of its Detox medicated soap; Detox White, Detox Green and Detox Orange. The company’s marketing specialist conducted a survey and gathered data which she utilized to estimate the following transition matrix. The matrix shows the probability of moving between brands each month: From White Green OrangeWhite 0.78 0.11 0.11 Green 0.04 0.94 0.02 Orange 0.20 0.04 0.76 The current (month 1) market shares are 50%, 20% and 30% for Detox White, Detox Green and Detox Orange respectively. Required (i) What will be the expected market shares for each of the three brands after two months have elapsed (that is, in month 3)?(ii) What is the long-run prediction for the expected market share for each of the three brands?4. ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) What is the probability that a filled bag will weigh less than 49.5 kilograms? (b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms? (c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled? (d) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?