A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels: Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I), and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data were subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Use $alpha = 0.01$
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The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.166 3.075 2.330 0.010 x1 0.228 0.302 0.755 0.000 x2 -1.184 0.586 -2.020 0.028 x3 -0.193 0.110 -1.755 0.114 x4 0.572 0.293 1.952 0.001 x5 -0.056 0.022 -2.545 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 1,847.24 369.4 5.60 0.000 Residual Error 41 2,704.20 65.96 Total 46 4,551.44 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm's work that is health care-related. a. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) y = 7.166 + 0.228x1 - 1.184x2 - 0.193x3 + 0.572x4 - 0.056x5 b. How large is the sample? How many independent variables are there? Sample N = 46 Independent variables k = 5 c-1. At the 0.05 significance level, state the decision rule to test: H0: β1 = β2 = β3 = β4 = β5 = 0; H1: At least one β is not 0. (Round your answer to 2 decimal places.) Reject H0 if the calculated F statistic is greater than the critical F value. c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) F statistic = 5.60 c-3. What is the decision regarding H0: β1 = β2 = β3 = β4 = β5 = 0? Reject H0, at least one regression coefficient is not equal to 0.
Shaiju T.
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. R^2: 0.519 Std. Error: 6.977 n: 64 ANOVA table: Source SS df MS F p-value Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11 Residual 3,018.3339 62 48.6828 Total 6,278.4320 63 Regression output: confidence interval variables coefficients std. error t Stat p-value Lower 95% Upper 95% Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252 X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563 (a) Write the fitted regression equation. (b-1) State the degrees of freedom for a two-tailed test for zero slope, and find the critical value at α = .05. (b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠0. (c-1) Calculate t. (c-2) Should the null hypothesis be rejected? (d-1) Find the 95% confidence interval for slope. (d-2) The confidence interval does not contain zero, which implies: - there is a relationship between the total assets (billions) and total revenue (billions). - there is no relationship between the total assets (billions) and total revenue (billions). (e-1) Calculate t^2 and F. (e-2) Calculate R^2. (e-3) What is the percentage of variation in total revenue explained by total assets?
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State the simple linear regression model. Verify manually the values of a and b given in the output: i. Provide 95% confidence intervals for a and b for the true regression model. ii. Comment on the significance of the slope parameter: Clearly justify your comment by using both the critical value and the p-value. iii. Interpret the sample correlation coefficient and the coefficient of determination; Comment on the significance of the overall regression model. Clearly justify your comment by using both the critical value and the p-value. (b) Consider the following Statistical output for multiple linear regression of literacy rate on number of newspapers, radios, and TVs (per 1000 population): Regression Summary for Dependent Variable: Literacy Rate R = 0.77978366 R-squared = 0.60806255 F-value = 5.1029 Standard Error = 0.11051 Number of Observations = 6 Intercept = 0.48888 Coefficient for Newspapers = 0.132007 Coefficient for Radios = 0.003440 Coefficient for TVs = 0.0047 Specify the multiple imputation model. Comment on the significance of the overall multiple regression model. Clearly justify your comment by using both the critical value and the p-value.
Madhur L.
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