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Multiple Linear Regression and Statistical Tests: Exercises and Questions, Exams of Nursing

Premiere Career CollegeNursing

A series of exercises and questions related to multiple linear regression and statistical tests, covering topics such as model parameters, assumptions, and common tests like chi-square and t-tests. It provides a valuable resource for students seeking to solidify their understanding of these concepts and practice applying them in real-world scenarios.

Typology: Exams

2024/2025

Available from 01/19/2025

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For ||the ||general ||form ||of ||multiple ||linear ||regression ||model, ||the ||fixed ||x1,
||x2,..., ||xi ||values, ||the ||y ||has ||a ||normal ||distribution ||with ||the ||what? ||- ||correct
||answer ||✔Variance ||and ||the ||mean
For ||the ||multiple ||linear ||regression ||model, ||each ||Bi ||can ||be ||interpreted ||as ||the
||true ||average ||change ||in ||y, ||EXCPET ||- ||correct ||answer ||✔Bo
For ||the ||multiple ||linear ||regression ||model, ||what ||happens ||when ||the ||xi
||increase ||by ||1 ||unit? ||- ||correct ||answer ||✔The ||values ||of ||all ||of ||the ||other
||predictors ||remain ||fixed
For ||the ||multiple ||linear ||model, ||what ||are ||considered ||parameters? ||- ||correct
||answer ||✔B0, ||B1, ||B3,... ||Bk
For ||the ||multiple ||Linear ||Model, ||what ||are ||considered ||as ||constant? ||- ||correct
||answer ||✔x1, ||x2, ||..., ||x1
For ||the ||sampling ||distribution ||of ||bi, ||bi ||has ||a ||normal ||distribution ||with ||the
||mean ||value ||of ||what? ||- ||correct ||answer ||✔Bi
For ||the ||sampling ||distribution ||of ||bi, ||the ||standard ||deviation ||of ||statistic ||bi,
||σi, ||involves ||what? ||- ||correct ||answer ||✔σ^2
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For ||the ||general ||form ||of ||multiple ||linear ||regression ||model, ||the ||fixed ||x1, ||x2,..., ||xi ||values, ||the ||y ||has ||a ||normal ||distribution ||with ||the ||what? ||- ||correct ||answer ||✔Variance ||and ||the ||mean For ||the ||multiple ||linear ||regression ||model, ||each ||Bi ||can ||be ||interpreted ||as ||the ||true ||average ||change ||in ||y, ||EXCPET ||- ||correct ||answer ||✔Bo For ||the ||multiple ||linear ||regression ||model, ||what ||happens ||when ||the ||xi ||increase ||by || 1 ||unit? ||- ||correct ||answer ||✔The ||values ||of ||all ||of ||the ||other ||predictors ||remain ||fixed For ||the ||multiple ||linear ||model, ||what ||are ||considered ||parameters? ||- ||correct ||answer ||✔B0, ||B1, ||B3,... ||Bk For ||the ||multiple ||Linear ||Model, ||what ||are ||considered ||as ||constant? ||- ||correct ||answer ||✔x1, ||x2, ||..., ||x For ||the ||sampling ||distribution ||of ||bi, ||bi ||has ||a ||normal ||distribution ||with ||the ||mean ||value ||of ||what? ||- ||correct ||answer ||✔Bi For ||the ||sampling ||distribution ||of ||bi, ||the ||standard ||deviation ||of ||statistic ||bi, || σi, ||involves ||what? ||- ||correct ||answer ||✔ σ ^

For ||the ||Multiple ||Regression, ||what ||is ||the ||variable ||selection? ||- ||correct ||answer ||✔Number ||of ||observations ||(or ||sample ||size ||= ||n), ||should ||be ||at ||least ||twice ||the ||number ||of ||predictors ||in ||the ||model. For ||the ||multiple ||regression, ||what ||is ||the ||model ||selection? ||- ||correct ||answer ||✔- ||All-subsets ||vs. ||Stepwise ||(forward, ||backward)

  • ||R^2, ||adjusted ||R^, ||and ||Mallow's ||Cp For ||the ||Multiple ||regression, ||what ||is ||the ||multicollinearity? ||- ||correct ||answer ||✔It ||is ||a ||strong ||linear ||relationship ||between ||values ||of ||the ||predictor ||variables For ||the ||multiple ||regression, ||what ||does ||multicollinearity ||causes? ||- ||correct ||answer ||✔It ||can ||cause ||instability ||of ||estimated ||coefficients ||as ||well ||as ||other ||problems For ||the ||multiple ||regression, ||what ||is ||diagnosis? ||- ||correct ||answer ||✔It ||is ||computing ||the ||R2 ||values ||for ||regressions ||in ||which ||the ||dependent ||variables ||is ||taken ||to ||be ||one ||of ||the ||k ||x's ||and ||the ||predictors ||are ||the ||remaining ||(k-1) ||x's. For ||the ||multipe ||regression, ||what ||happends ||when ||the ||diagnosis ||R2 ||is ||large? ||- ||correct ||answer ||✔If ||it ||close ||to ||1, ||then ||it ||proves ||that ||the ||multicollinearity ||exists. What ||are ||the ||four ||common ||types ||of ||biological ||data? ||- ||correct ||answer ||✔- ||Nominal ||(categorical)

(Used ||to ||test ||whether ||individuals ||that ||have ||one ||characteristic ||also ||tend ||to ||have ||another ||one)

  • ||Comparison ||of ||proportions (Used ||to ||test ||whether ||the ||proportion ||of ||individuals ||with ||some ||characteristics ||are ||same ||in ||different ||populations What ||are ||the ||assumptions ||of ||chi-square ||test? ||- ||correct ||answer ||✔- ||Random ||samples
  • ||Independent ||observations ||on ||one ||or ||more ||categories.
  • ||Chi-square ||test ||requires ||numerical ||values ||(counts), ||NOT ||PERCENTAGES ||OR ||RATIO.
  • ||Chi-square ||should ||not ||be ||calculated ||if ||the ||expected ||value ||in ||any ||category ||is ||less ||than || 5
  • ||Adequate ||sample ||size For ||the ||chi-square ||testing, ||the ||univariate ||categorical ||data ||are ||conveniently ||summarized ||in ||what? ||- ||correct ||answer ||✔one-way ||frequency ||table For ||the ||chi-square ||testing, ||if ||there ||are ||two ||different ||categorical ||variables, ||what ||happends? ||- ||correct ||answer ||✔You ||will ||get ||a ||two-way ||frequency ||table, ||which ||is ||call ||a ||contingency ||table

For ||the ||Chi-square ||Distribution, ||the ||chi-square ||curve ||has ||no ||area ||associated ||with ||what ||kind ||of ||value? ||- ||correct ||answer ||✔Negative For ||the ||chi-square ||distribution, ||what ||kind ||of ||symmetry ||does ||the ||chi-curve ||have? ||- ||correct ||answer ||✔Asymmetric For ||the ||chi-square ||distribution, ||what ||is ||the ||chi-square ||curve ||defined ||by? ||- ||correct ||answer ||✔df ||(degree ||of ||freedom) For ||the ||chi-square ||testing, ||when ||the ||Ho ||is ||true ||the ||expected ||counts ||should ||be ||at ||least ||what? ||- ||correct ||answer ||✔ 5 What ||are ||the ||steps ||for ||solving ||chi-square ||test? ||- ||correct ||answer ||✔1. ||Write ||the ||observed ||frequencies ||in ||column ||O

  1. ||Figure ||the ||expected ||frequencies ||and ||write ||them ||in ||column ||E
  2. ||Use ||the ||formula ||to ||calculate ||the ||chi-squared ||statistic: ||X^
  3. ||Find ||the ||df ||(N-1)
  4. ||Find ||the ||table ||value ||(consult ||the ||Chi0Square ||Table)
  5. ||If ||your ||chi-square ||value ||is ||equal ||to ||or ||greater ||than ||the ||table ||value, ||reject ||the ||null ||hypothesis: ||difference ||in ||your ||data ||are ||not ||due ||to ||chance ||along

For ||the ||nonparametric ||test, ||since ||that ||the ||nonparametric ||test ||compares ||with ||the ||median, ||what ||does ||that ||mean? ||- ||correct ||answer ||✔As ||a ||result, ||if ||the ||data ||has ||one ||or ||two ||outliers, ||their ||influence ||is ||canceled. What ||are ||the ||limitations ||for ||a ||nonparametric ||test? ||- ||correct ||answer ||✔- ||Less ||powerful ||comparing ||to ||the ||parametric ||test, ||which ||only ||detects ||the ||difference.

  • ||It ||requires ||a ||large ||sample ||sizes ||to ||improve ||the ||statistical ||power, ||the ||likelihood ||of ||obtaining ||significant ||results ||if ||there ||is ||difference ||between ||populations. What ||is ||the ||basic ||assumptions ||for ||nonparametric ||test? ||- ||correct ||answer ||✔- ||The ||two ||populations/treatments ||response ||distributions ||have ||the ||same ||shape ||and ||spread.
  • ||The ||difference ||in ||the ||distribution ||is ||the ||shape ||of ||the ||graph ||is ||either ||the ||same ||or ||shifted What ||is ||the ||Mann-Whitney ||U ||test? ||- ||correct ||answer ||✔- ||It ||an ||alternative ||for ||unpaired ||two ||sample ||t-test ||(equal ||or ||unequal ||sample ||size)
  • ||The ||actual ||measurements ||are ||not ||employed, ||instead ||we ||use ||the ||ranks ||of ||measurements.
  • ||The ||data ||can ||be ||ranked ||either ||from ||lowest ||to ||highest
  • ||It ||actually ||test ||if ||two ||populations ||have ||same ||distribution. What ||is ||the ||Kruskal-Wallis ||Test? ||- ||correct ||answer ||✔- ||It ||an ||alternative ||for ||one-way ||ANOVA ||and ||also ||known ||as ||analysis ||of ||variance ||by ||ranks ||
  • ||It ||to ||test ||that ||whether ||the ||means ||may ||be ||concluded ||to ||be ||different ||from ||each ||other
  • ||However, ||it ||addresses ||the ||more ||general ||questions ||of ||whether ||the ||sampled ||populations ||have ||a ||DIFFERENT ||DISTRIBUTIONS. What ||is ||the ||Spearmen's ||rank ||correlation? ||- ||correct ||answer ||✔- ||It ||is ||an ||alternative ||to ||Pearson's ||product ||moment ||correlation.
  • ||The ||data ||obtained ||from ||the ||bivariate ||population ||that ||is ||far ||from ||a ||normal ||distribution, ||then ||the ||Pearson ||correlation ||is ||inapplicable.
  • ||There ||is ||also ||NO ||ASSUMPTIONS ||ABOUT ||THE ||SHAPES ||OF ||DISTRIBUTIONS, ||data ||can ||be ||measurable, ||counts, ||or ||ordinal ||data