Problem 1: Determine the least squares data fit for the following data. Also, find the root- mean-square-error of your least square fit. Xi yi -1.466 0.3 -0.062 0.6 0.492 0.9 0.822 1.2 1.068 1.5 1.944 1.8 2.583 2.1 3.239 2.4 4.148 2.7 4.464 3 5.185
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- Question 5 (c) How does the size of the data set help cut down on the size of the error terms in the approximation process?Calculate the PRESS statistic for the model developed from the estimation data in Problem 11.2. How well is the model likely to predict? Compare this indication of predictive performance with the actual performance observed in Problem 11.2.The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm
- The operations manager of a musical instrument distributor feels that the demand for Bass Drums may be related to the number of television appearances by the popular rick group Green Shades during the previous month. The manager has collected the data shown in the following table. Demand for Bass Drums 3 6 7 5 10 8 Green Shades TV appearances 3 4 7 6 8 5 Develop the linear regression equation to forecast. Forecast demand for Bass Drums when Green Shades’ TV appearances are 10. Compute MSE and standard deviation for Problem 8.problem 1 A local health centre noted that in a sample of 400 patients, 80 were referred to them by the localhospital.a. Provide a 95% confidence interval for all the patients who are referred to the health centre bythe hospital. b.What sample size would be required to estimate the proportion of all hospital referrals to thehealth centre with a margin of error of 0.04 or less at 95% confidence? problem 2 The data in the table below presents the hourly quantity of production for three lines of productionprocesses over the first 4 days in XYZ Company. Answer the questions based on the Excel Output givenbelow. Day Process 1 Process 2 Process 31 33 33 282 30 35 363 28 30 304 29 38 34 a.State the null and alternative hypothesis for single factor ANOVA.b. State the decision rule (α = 0.05).c. Calculate the test statistic. d. Make a decision.An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and gathers the following data a. Construct a scatter plot. b. Use the least-squares method to determine the regression coefficients b0 and b1 c. Interpret the meaning of and in this problem. d. Predict the monthly rent for an apartment that has 1,000 square feet
- Although the Excel regression output, shown in Figure 12.21 for Demonstration Problem 12.1, is somewhat different from the Minitab output, the same essential regression features are present. The regression equation is found under Coefficients at the bottom of ANOVA. The slope or coefficient of x is 2.2315 and the y-intercept is 30.9125. The standard error of the estimate for the hospital problem is given as the fourth statistic under Regression Statistics at the top of the output, Standard Error = 15.6491. The r2 value is given as 0.886 on the second line. The t test for the slope is found under t Stat near the bottom of the ANOVA section on the “Number of Beds” (x variable) row, t = 8.83. Adjacent to the t Stat is the p-value, which is the probability of the t statistic occurring by chance if the null hypothesis is true. For this slope, the probability shown is 0.000005. The ANOVA table is in the middle of the output with the F value having the same probability as the t statistic,…Problem 1: In 2008, data from the Center for Disease Control revealed that 28.5% of all male teenagers, aged 18-19 and attending U.S. colleges were overweight. The definition of overweight is a body mass index (BMI) of over 25. In 2019, a professor in public health at a major university wanted to determine whether that proportion had decreased since 2008. So, he sampled 800 randomly selected incoming male freshman at universities around the country. Using the BMI measurements, he found that 210 of them were overweight. Test the professor’s claim at an α = 0.05 level of significance, the proportion of obese male teenagers in American colleges decreased. Make sure that any necessary assumptions for conducting the hypothesis test are satisfied. A) State the null and alternative hypothesis. H0: Ha: B) Determine the critical value(s) for the test. C) Compute the test statistic (show…For items 1 - 5, use the data below that gives the humerus bone length (in cm) and height (in inches) for a sample of female skeletons. [The data was provided by Dr. Ayers-Darling, former professor at MVCC.] humerus (cm) height (in.) 32.6 66 28.0 60 29.9 62 30.5 63 31.2 64 29.9 62 29.1 61 29.5 62 29.8 62 28.5 61 Find the slope of the least-squares regression line that relates humerus length to female height. Express its value to three decimal places (to the nearest thousandth).__________________________ Find the y-intercept of the least-squares regression line that relates humerus length to female height. Express its value to three decimal places (to the nearest thousandth).___________________________ The least-squares regression line relating two variables x and y is given by . Find the predicted value of y if x is 2.___________
- Problem 3 addressed the cross-sectional variation in the number of financial analysts who follow a company. in that problem, company size and debt-to-equity ratios were the in- dependent variables. you receive a suggestion that membership in the S&P 500 index should be added to the model as a third independent variable; the hypothesis is that there is greater demand for analyst coverage for stocks included in the S&P 500 because of the widespread use of the S&P 500 as a benchmark. a. write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index. also include company size and debt-to-equity ratio in this equation. use the notations below. (analyst following)i = natural log of (1 + number of analysts following company i) Sizei = natural log of the market capitalization of company i in millions of dollars (d/e)i = debt-to-equity ratio for company i S&Pi = inclusion of company i in the S&P…Question 2 Ignore the term "maximum likelihood"Problem 3: Please answer parts a, b, and c! A sample of 136 hypertensive people were given an anti-hypertensive drug, and the drug was found to be effective in 49 of those people. (By effective, we mean that their diastolic blood pressure is lowered by at least 10 mm Hg as judged from a repeat measurement taken 1 month after taking the drug.) (a) Find a 90% confidence interval for the true proportion of the sampled population for which the drug is effective. (b) Using the results from the above mentioned survey, how many people should be sampled to estimate the true proportion of hypertensive people for which the drug is effective to within 4% with 96% confidence? (c) If no previous estimate of the sample proportion is available, how large of a sample should be used in (b)?