Mathematics > QUESTIONS & ANSWERS > Exam Review > Midterm 2021 Sol National University of Singapore: ST5202 Applied Regression Analysis (All)

Exam Review > Midterm 2021 Sol National University of Singapore: ST5202 Applied Regression Analysis Semester II, 2020-2021

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PAGE 2 ST5202 1. A person’s muscle mass is expected to derease with age. To explore this relationship in women, a nutritionist randomly selected 16 women with age 40 to 79. The data is created as ... a data frame object muscle.dat in R with variable names mass and age. The following are the results obtained by the lm function: lm(formula = mass ~ I(age - 40), data = muscle.dat) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 107.1071 4.3752 24.480 6.84e-13 *** I(age - 40) -1.0236 0.1882 -5.439 8.72e-05 *** Residual standard error: 8.344 on 14 degrees of freedom Multiple R-squared: 0.6788, Adjusted R-squared: 0.6559 F-statistic: 29.59 on 1 and 14 DF, p-value: 8.721e-05 (i) From the information provided above, (ii) [2 + 2 + 2 = 6 marks] Test whether or not there is a linear relationship between mass and age at level α = 0:001. State the null and alternative hypothesis in terms of the parameters in the regression function, provide the test statistic and its value, give the decision rule and your conclusion. H0 : β1 = 0, H1 : β1 6= 0. The test statistic: T = β^1 s:d:(β^1) = −5:439: Decision rule: if the p-value 2P(t14 > 5:439) < 0:001, reject H0, otherwise, do not reject. Conclusion: since the p-value 8.72e-05 is less than 0.001, reject H0. (iii) [2 + 2 + 2 = 6 marks] Test whether or not mass is negatively related to age. State the null and alternative hypothesis in terms of the parameters in the regression function, provide the test statistic and its value, give the p-value of the test and your conclusion. 3 [Show More]

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