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- The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Coef SE Coef T PConstant 0.8570 0.4148 2.06 0.84Weight 0.38243 0.02978 13.52 0.000 S = 0.517508 R-Sq = 97.4% (a) Write out the least-squares equation. y^= ______ + _____x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)Consider the following regression model Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4Xt + ∈t , where U, V, W, X and Y are economic variables observed from t = 1, . . . , 75, β0 , . . . , β4 are the model parameters and ∈t is the random disturbance term satisfying the classical assumptions. Ordinary Least Squares (OLS) is used to estimate the parameters, producing the following estimated model: Yt = 1.115 + 0.790*Ut − 0.327*Vt + 0.763*Wt + 0.456*Xt (0.405) (0.178) (0.088) (0.274) (0.017) where standard errors are given in parentheses, the R-squared = 0.941, the Durbin-Watson statistic is DW = 1.907 and the residual sum of squares is RSS = 0.0757. In answering this question, use the 5% level of significance for any hypothesis tests that you are asked to perform, state clearly the null and al- ternative hypotheses that you are testing, the test statistics that you are using and interpret the decisions that you make.…The position of a particle x(t) on an axis has been monitored. The results are shown in the following table. t x(t)0 41 114 129 12 By the least squares method, fit the data to a quadratic model: Report x(10)
- Table 14.17 The Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval. Calculate the 99 percent confidence interval for…The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Coef SE Coef T P Constant 0.8489 0.4148 2.06 0.84 Weight 0.39782 0.02978 13.52 0.000 S = 0.517508 R-Sq = 96.6% (a) Write out the least-squares equation. = + x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)(c) What is the value of the correlation coefficient r? (Use 3 decimal places.)The following data give the diffusion time (hours) ofa silicon wafer used in manufacturing integrated circuitsand the resulting sheet resistance of transfer:Diffusion time, x 0.56 1.10 1.58 2.00 2.45Sheet resistance, y 83.7 90.0 90.2 92.4 91.6(a) Find the equation of the least squares line fit to thesedata.(b) Predict the sheet resistance when the diffusion time is1.3 hours.
- The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…Find the least-squares equation for the following pairs of data: x = earthquake magnitude 2.9 4.2 3.3 4.5 2.6 3.2 3.4 y = depth of earthquake (in km) 5 10 11.2 10 7.9 3.9 5.5 A. y = 2.16 + 0.221x B. y = 0.221 + 2.16x C. y = 2.16 + 0.312x D. y = 0.221 + 2.82xFor b there are two cases and for c I have to plug the initial data into the ode
- Given the table of data points x −1 1 2 y 1 3 3 find the best least squares fit by a linear function f (x) = c1 + c2x.. From the Exerrise 6.2(1). find the regression line using the least squares 11 lerhod . Interpret the result. Then. estimate the ntunber of hours he or she exercises per \\"week \vhen his or her age is 50 years old. Exercise 6.2(1). Age. x 18 26 32 38 52 59 Hours. y 10 5 -1 3 1. 5 1To this point, the work of days missed per month by workers at a large corporation has average 2.25. A new flexible workday arrangement has been introduced and it is hoped that by introducing this "flex time" that the average workdays miss per month will be reduced. Let alpha=.05 A) Define the appropriate parameter for this problem and then set up the appropriate Null and alternative hypothesis a. The average number of work days missed by all the workers at a large corporation. Ho: x bar= 2.25; Ha: x bar < 2.25 b. the Average number of work days missed by all workers at a large corporation Ho: mu =2.25; Ha: mu < 2.25 c. Number of workdays mess by the workers d. The average number of workdays mess by the 20 workers at a large corporation Ho: mu =2.25 ; Ha: mu> 2.25 B) Flex time is tried out with a sample of 20 workers. The average number of days missed in the next month is 1.83 with a standard deviation of 0.71. Make any necessary assumptions and use the data to (a) calculate…