Regression AnalysisQuiz 7 Name: ANSWER KEYStat 217SSTSSMR 2 ibiSEbt MSEMSMF A group of medical researchers are interested in studying how the weight (in pounds) and age (in years) of male patients (of approximately the same height) relate to systolic blood pressure (in mmHg, millimeters of mercury). From a SRS of males, we have the following output from MINITAB:Regression AnalysisPredictor Coef StdErr T PConstant -65.10 14.94 ***** 0.001Weight 1.07710 0.07707 ***** 0.000Age 0.42541 0.07315 **** 0.000S = 2.509 R-Sq = 95.7% R-Sq(adj) = 94.9%Analysis of VarianceSource DF SS MS F PRegression 2 1423.84 711.92 ****** 0.000Residual Error ** 62.93 6.29Total 12 1486.771. How many men were used in the study?DFT = n-1 = 12, so n=13 men were used in the study.2. Estimate the systolic blood pressure of a male who weighs 170 pounds and is 35 years old. Use proper units in your answer. -65.1 + 1.0771(170) + .42541(35) = 132.896 mmHg.3. Perform the first and most important hypothesis test of interest:- State the hypotheses. H0: 021Ha: i is not zero for some i - Find the test statistic. t = 711.92/6.29 = 113.18- What is the distribution of the test statistic given that the null hypothesis is true? F ~ F(2,10)- Give the p-value. p-value = 0.000- Make a conclusion in terms of the problem . The evidence suggests that there is a linear relationship between systolic blood pressure and at least one of either weight or age.4. Is it appropriate to conduct the follow-up test for the linear relationship between age and systolic blood pressure? Why or why not?Since we rejected H0 in #3, then it is appropriate to perform follow-up tests on age (and weight).5. Conduct the follow-up test for the linear relationship between age and systolic blood pressure- State the hypotheses.H0: 02Ha: 02- Find the test statistic.t = .42541/.07315 = 5.816- What is the distribution of the test statistic given that the null hypothesis is true?t ~ t(10)- Give the p-value.0.000- Make a conclusion in terms of the problem. The evidence suggests that there is a linear relationship between age and systolic blood pressure given that weight is in the model.6. Interpret the coefficient for weight in terms of the problem using proper units.Among men of the same age, for each additional pound of weight, systolic blood pressure increases on average by 1.077 mmHg.7. Is this MLR a good model for predicting systolic blood pressure? Why or why not?Since both predictors are significant, and since R2 = 95.7% of the variability of systolic blood pressure is explained by the model, then this is a very good model
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