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Problem 2: A study was undertaken to assess the quality of cheese as determined by a panel of taste testers. The tasters rated samples

 

Problem 2: A study was undertaken to assess the quality of cheese as determined by a panel of taste testers. The tasters rated samples of cheese as being acceptable or not acceptable. Those same samples of cheese were analyzed with respect to several variables, one of which was the untransformed concentration of lactic acid, designated as Lactic. A logistic regression was fitted relating the log odds that the cheese was acceptable to the explanatory variable Lactic. The following partial output is provided: Term Intercept Lactic Parameter Estimates Estimate -10.779932 0.6331925 Std Error 3.9754177 0.24531656 1. What is the meaning of the entry, 0.6332 in the above table under "Estimate" for the variable "Lactic"? 2. A sample of cheese was analyzed and the variable Lactic was found to have the value 16.5. At this level of concentration of lactic acid, what are the odds that the cheese will be deemed to be acceptable? 3. What is the approximate 90% confidence interval estimate for the true slope of the logistic regression model? 4. What is the value of the test statistic and the P value for the test of the hypotheses: Ho: 0. Ha: B10 5. Which of the following statements concerning statistical inference for logistic regression is (are) FALSE? (a) A level C confidence interval for the slope B is given by b z SEb * (b) To test Ho: B1 = 0, the test statistic is given by z = (c) The level C confidence interval for the odds ratio e is given by e z eSE (d) The Ho: B1=0 is equivalent to testing the null hypothesis Ho: "The odds ratio is 1".. (e) The level C confidence interval for the odds ratio e is given by (e-SE,+SE) Problem 2: A study was undertaken to assess the quality of cheese as determined by a panel of taste testers. The tasters rated samples of cheese as being acceptable or not acceptable. Those same samples of cheese were analyzed with respect to several variables, one of which was the untransformed concentration of lactic acid, designated as Lactic. A logistic regression was fitted relating the log odds that the cheese was acceptable to the explanatory variable Lactic. The following partial output is provided: Term Intercept Lactic Parameter Estimates Estimate -10.779932 0.6331925 Std Error 3.9754177 0.24531656 1. What is the meaning of the entry, 0.6332 in the above table under "Estimate" for the variable "Lactic"? 2. A sample of cheese was analyzed and the variable Lactic was found to have the value 16.5. At this level of concentration of lactic acid, what are the odds that the cheese will be deemed to be acceptable? 3. What is the approximate 90% confidence interval estimate for the true slope of the logistic regression model? 4. What is the value of the test statistic and the P value for the test of the hypotheses: Ho: 0. Ha: B10 5. Which of the following statements concerning statistical inference for logistic regression is (are) FALSE? (a) A level C confidence interval for the slope B is given by b z SEb * (b) To test Ho: B1 = 0, the test statistic is given by z = (c) The level C confidence interval for the odds ratio e is given by e z eSE (d) The Ho: B1=0 is equivalent to testing the null hypothesis Ho: "The odds ratio is 1".. (e) The level C confidence interval for the odds ratio e is given by (e-SE,+SE)

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