STAT551 - Summer 2016 Computer Homework #3 Due: August 12 N.B. assignments emailed past this date will not be accepted Use the same database as the last computer homework to answer the following questions. Be sure to follow the instructions from the first computer homework. The numbers in () represent the points for each part. There are a total of 45 points for this homework. Remember to read the comments embedded in the provided R code (after the #). You may also need to refer to past computer assignments - these assignments are cumulative. Originally, this data set was constructed from NHANES to see if the claim that obesity is increasing in American children and to examine the role sugar plays (sugar appears to be the present day focus for the obesity 'crisis'). We will look at BMI in two different ways: 1. the BMI measurement itself and 2. the age and sex adjusted categorization of BMI into obese, overweight, normal and underweight. Answer each question using the R code provided. Some instructions for the R code is provided in the comment (after the #), so please read this part as well. Remember, this is a statistics class, a yes/no answer or one based on opinion is insufficient. Use the appropriate statistical techniques you have learned to answer questions 1 to 6. For each of these questions: 1. report the statistical test used; 2. in prose, state the null hypothesis; 3. report the results of the test; and 4. what you conclude vis a vis the hypothesis given results of the test - also in prose. You may use bullets to report out each of the 4 parts above. Question 7 does not require the 4 parts above. For all 7 questions, you must include (cut and paste) the computer results you used to answer the questions. 1. According to one study, the prevalence of obesity among 5 - 11 years old US children in 1988 - 1994 was 15.1. Your data set is from the years 2011 - 2012. Does your estimate of the obesity prevalence in 2011 - 2012 uphold the contention that obesity has increased since the earlier period? Statistical Test Used: Null Hypothesis: The estimate of the obesity prevalene in 2011-2012 does not uphold the contention that obesity has increased since the earlier period. True p is Equal to 0.151 Results of the Test: Do Not Reject the Null Hypothesis Conclusion: There is not enough evidence to reject that the estimate of the obesity prevalence in 2011-2012 does not uphold the contention that obesity has increased since the earlier period. Computer Results: 1-sample proportions test with continuity correction data: 257 out of 1385, null probability 0.151 X-squared = 12.635, df = 1, p-value = 0.0003786 alternative hypothesis: true p is not equal to 0.151 95 percent confidence interval: 0.1656208 0.2072684 sample estimates: p 0.1855596 2. Is BMI different by sex for children 5 years old? Statistical Test: Null Hypothesis: BMI is not different by sex for children 5 years old. Test Results: Conclusion: Computer Results Welch Two Sample t-test data: BMXBMI by RIAGENDR t = -0.42898, df = 149.97, p-value = 0.6686 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.7842566 0.5044705 sample estimates: mean in group 1 mean in group 2 15.89647 16.03636 3. Is BMI different for those whose family income is below a living wage when compared to children whose family incomes are in the highest level (more than 4 times the poverty level)? Statistic Test: Null Hypothesis: Test Results Conclusion: Computer Results Welch Two Sample t-test data: BMXBMI by inc t = 6.4958, df = 440.96, p-value = 2.233e-10 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 1.228513 2.294399 sample estimates: mean in group 1 mean in group 3 18.80866 17.04721 4. If we use categories of BMI and compare the obesity by sex do we come to the same conclusion as in #2? income as in #3? Statistic Test: Null Hypothesis: Test Results Conclusion: Computer Results 1 2 1 23.28231 22.71769 2 443.88231 433.11769 3 103.75812 101.24188 4 130.07726 126.92274 Pearson's Chi-squared test data: bmi$BMDBMIC and bmi$RIAGENDR X-squared = 1.0599, df = 3, p-value = 0.7868 Fisher's Exact Test for Count Data data: bmi$BMDBMIC and bmi$sugrec p-value = 0.4897 alternative hypothesis: two.sided 1 3 1 29.10117 6.898833 2 513.31226 121.687743 3 131.76362 31.236381 4 156.82296 37.177043 Pearson's Chi-squared test data: incd$BMDBMIC and incd$inc X-squared = 23.795, df = 3, p-value = 2.756e-05 Fisher's Exact Test for Count Data data: incd$BMDBMIC and incd$inc p-value = 8.173e-06 alternative hypothesis: two.sided 5. This data was collected to see if sugar is highly associated with BMI in children - a claim widely touted. Does the NHANES data support that hypothesis? Statistic Test: Null Hypothesis: Test Results Conclusion: Computer Results 1 2 3 1 0.2875399 22.42812 22.28435 2 5.0607029 394.73482 392.20447 3 1.1884984 92.70288 92.10863 4 1.4632588 114.13419 113.40256 Pearson's Chi-squared test data: bmi$BMDBMIC and bmi$sugrec X-squared = 5.0334, df = 6, p-value = 0.5395 Fisher's Exact Test for Count Data data: bmi$BMDBMIC and bmi$sugrec p-value = 0.4897 alternative hypothesis: two.sided In a course on multiple linear regression (offered in-class at the SPH) we would be able to analyze this data in a more thorough (and proper) manner. However, for the purposes of this class, we will start the process. First, the variables we are interested in for the next two questions are bmi, sugar use, sex, income and age. 6. Which of the variables of interest are correlated to bmi? {THINK. What types of variables can be used in a correlation?} Statistic Test: Null Hypothesis: Test Results Conclusion: Computer Results Pearson's product-moment correlation data: bmi$BMXBMI and bmi$sugrec t = -5.3364, df = 1250, p-value = 1.125e-07 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.20296817 -0.09462569 sample estimates: cor -0.1492448 7. Which of the variables of interest can be used to predict a child's bmi? If a variable is not statistically significant, remove that variable and rerun the regression. Write out the resulting equation. What is the predicted bmi value for a 7.3 year old boy whose income ratio is 1.9. For reasons outside the basic introductory level of regression in this class, sugar cannot be used as is in a regression model? Computer Results Call: lm(formula = BMXBMI ~ RIAGENDR + INDFMPIR + RIDEXAGM, data = bmi) Residuals: Min 1Q Median 3Q Max -9.1170 -2.5737 -0.9687 1.4973 27.0512 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 12.144812 0.602216 20.167 < 2e-16 *** RIAGENDR 0.139219 0.224751 0.619 0.536 INDFMPIR -0.420808 0.073403 -5.733 1.23e-08 *** RIDEXAGM 0.067721 0.004761 14.223 < 2e-16 *** --Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 4.039 on 1289 degrees of freedom (92 observations deleted due to missingness) Multiple R-squared: 0.1503, Adjusted R-squared: 0.1483 F-statistic: 76 on 3 and 1289 DF, p-value: < 2.2e-16 qattachments_511dc3fe150869410d2180391def9c3aeb99a538 SEQN MCQ010 BMXBMI BMDBMIC RIAGENDR RIDRETH1 RIDEXAGM INDFMPIR timehere 62166 2 16.2 2 1 3 120 4 62168 1 15.4 2 1 5 81 3.48 4 62175 2 16.7 2 1 3 72 0.39 4 62181 2 16.4 2 1 1 118 0.55 4 62183 2 16.1 2 1 4 81 3.6 4 62187 2 16.4 2 2 1 115 4 62192 1 26.7 4 2 1 141 2.05 4 62194 2 14.7 2 2 3 113 5 4 62198 2 17.4 2 1 3 93 0.61 4 62203 2 16.2 2 1 4 99 4 62245 2 15.3 2 1 5 97 5 4 62252 2 16 2 2 1 143 2.62 4 62260 2 14.9 2 1 3 125 5 4 62271 1 24.1 4 1 4 87 1.63 4 62272 2 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