PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU Albe M Inbc M (6e3 3an Das | + PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... IMG_4261.jpg 1 3 Problem 1 (15) The following data give percentage of women working in five companies (x) in the retail and trade industry. The percentage of management jobs (y) held by women in each company is also shown. x = = % Working 67 45 73 54 61 y = % Management 49 21 65 47 33 Answer a) and c)-f) by doing your own calculations without using Minitab. Show these calculations in the submitted assignment. a) The least squares line for the data in the above table has a slope B = 1.3. What is the y-intercept 30 of that line? (3) b) Interpret coefficients Bo and B.(2) c) Find the five fitted values and five residuals. What is the sum of the residuals? (3) d) Computes, the standard error of regression. What is the interpreta- tion of s and what does s estimate? (3) Sy. e) Compute sy and interpret it. Compare s with What do you see from this comparison? (3) f) In general, what is the approximate percentage of data points that should lie within s (2s) of the least squares line? In this exercise, how many data points lie within s (2s) of the least squares line? (3) PGA (2).xlsx IMG_4257.jpg P IMG_4258.jpg EN 3C Clear > (8) POFUS A ... 23:02 01.12.2022 PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU Albe M Inbc M (6e3 3an Das | + PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... IMG_4261.jpg 1 3 Compute by ana CU 10. VV IIo you Do from this comparison? (3) f) In general, what is the approximate percentage of data points that should lie within s (2s) of the least squares line? In this exercise, how many data points lie within s (2s) of the least squares line? (3) Problem 2 (4) MBS, Ex 11.82 on page 666 Spreading rate of spilled liquid The data for this problem is in the attached file LSPILL. PGA (2).xlsx 1 IMG_4257.jpg IMG_4258.jpg P x EN 3C Clear > (8) POFUS A 23:02 01.12.2022 PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU Albe M Inbc M (6e3 3an Das | + 0 PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... IMG_4261.jpg 2 3 Problem 3 (11) Financial institutions charge, in general, different interest rates on their loans. A financial analyst was interested in the relationship between Y and X, where Y = X = the default rate per 1000 loans (i. e. the number of loans that default per 1000 loans) the interest rate (%) on a loan. She collected data on a random sample of financial institutions, that is, for each institution in the sample she recorded the interest rate charged by that institution and the number of defaults per 1000 loans given by that institution. Answer the following questions using the Minitab output on the next page. a) Interpret the regression coefficients in the estimated model. (2) b) Is there a statistically significant linear relationship between Default rate and Interest rate? Test at a = 0.01 (State Ho and H, the rejection rule of the test and your conclusion.) (3) c) What proportion of variation in Y is explained by the model? What is the sample correlation coefficient between Y and X? (2) d) A banker claims that for every 1 percentage increase in Interest rate the expected change in Default rate is 7 loans. Based on the estimated PGA (2).xlsx IMG_4257.jpg P IMG_4258.jpg EN 3C Clear ^ (8) POFUS A 23:02 01.12.2022 PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU Albe M Inbc M (6e3 3an Das | + PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... 0 IMG_4261.jpg 2 3 + that default per 1000 10 X = the interest rate (%) on a loan. She collected data on a random sample of financial institutions, that is, for each institution in the sample she recorded the interest rate charged by that institution and the number of defaults per 1000 loans given by that institution. Answer the following questions using the Minitab output on the next page. a) Interpret the regression coefficients in the estimated model. (2) b) Is there a statistically significant linear relationship between Default rate and Interest rate? Test at a = 0.01 (State Ho and H, the rejection rule of the test and your conclusion.) (3) c) What proportion of variation in Y is explained by the model? What is the sample correlation coefficient between Y and X? (2) d) A banker claims that for every 1 percentage increase in Interest rate the expected change in Default rate is 7 loans. Based on the estimated model can you reject his claim? (Answer by constructing an appropriate 95% confidence interval or by using a hypothesis with the significance level a = 0.05).(3) e) Estimate the expected default rate on loans of financial institutions, which charge interest rate of 9%. Is this a valid estimate? Explain. (3) PGA (2).xlsx IMG_4257.jpg P x IMG_4258.jpg EN 3C Clear > (8) POFUS A 23:02 01.12.2022 PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU * Albe M Inbc | M (6e3 3an 0 Das | + PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... IMG_4261.jpg 3 3 ^ Regression Analysis: DEFAULT RATE versus INTEREST RATE DEFAULT RATE = 4.57 + 4.945 INTEREST RATE Coefficients Term Coef SE Coef T-Value P-Value Constant 4.57 INTEREST RATE 4.945 7.23 0.994 0.63 4.97 0.548 0.002 Analysis of Variance Source DF SS Regression 1 132.517 Error 7 37.483 Total 8 170.000 Model Summary S 2.31404 R-sq Regression Equation PGA (2).xlsx IMG_4257.jpg IMG_4258.jpg P x EN 3C Clear ^ (8) POFUS A 23:03 01.12.2022 PUS A8.p Com Com = Com Anti Final + Com Quiz ITBS NYU * Albe M Inbc | M (6e3 3an Das | + 0 PDF Viewer chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://brightspace.nyu.edu/d2l/common/viewFile.d2lfile/Database/... IMG_4261.jpg 3 3 Descriptive Statistics: DEFAULT RATE, INTEREST RATE Variable N N* Mean SE Mean StDev Minimum DEFAULT RATE 9 0 40.33 INTEREST RATE 9 0 7.233 1.54 0.274 4.61 0.823 35.00 6.000 Maximum 48 8.500 PGA (2).xlsx IMG_4257.jpg IMG_4258.jpg P x EN 3C Clear ^ (8) POFUS A 23:03 01.12.2022 BCTABKA LSPILL (3) [ ] Excel ( ) : . , . ? 1. - 14 fx A 1 TIME B C D E F G H | J K L M N P Q R S MASS 11 2468021222223344658 2345678901234567808222222222 0 6,64 1 6,34 6,04 5,47 4,94 4,44 3,98 3,55 3.15 2,79 2,45 2,14 1,86 1,6 1,37 1,17 0,98 0,6 0,34 0,17 0,06 55 0,02 0 Sheet1 P EN x 3C Clear > (8) 23:05 01.12.2022 + 100% BIA Google Calender Google Drive Stern Apps Thesaurus Grammarly Statistics Textboo 1 0 x 0.24 0.25 0.26 0.27 0.28 0.29 0.3 NRMSE LSPILL 11.82 SPREADING RATE OF SPILLED LIQUID. Refer to the Chemical Engineering Progress (January 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise 11.30 (p. 644) and the data saved in the file. Find and interpret r and r2 for the simple linear regression y= mass of the spill and x = elapsed time of the spill. Applying the Concepts-Advanced NW 11.83 SALARY LINKED TO HEIGHT. Are short people short-changed when it comes to salary? According to researchers, tall people tend to earn more money over their careers than short people (Journal of Applied Psychology, June 2004). Using data collected from participants in the National Longitudinal Surveys, the researchers computed the correlation between average earnings (in dollars) and height (in inches) for A tv Search or tune UIDI EA