MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis., Exams of Nursing

Download MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. and more Exams Nursing in PDF only on Docsity! MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. Course Project: Part C Week 7 MATH 534 : Applied Managerial Statistics Keller Graduate School of Management MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. Regression and Correlation Analysis MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. P Value = 0.000 ANOVA df SS MS F Significance F Regression 3 278.1888971 92.72963236 3.985922758 0.010080614 Residual 96 2233.371103 23.26428232 Total 99 2511.56 6. Based on the findings in Steps 1-5, analyze the ability of the independent variable to predict the designated dependent variable. There is a strong positive relationship between sales and calls. R² = 0.0722. The amount of calls is a good metric for forecasting of sales. There is a direct positive linear relationship between calls and sales. 7. Compute the confidence interval for β1 (the population slope) using a 95% confidence level. Interpret this interval. The confidence interval for a 95% confidence level for 150 calls the average sales calls per week falls between 40.78% and 42.99%. The can expect at least 41.86% sales a week. 8. Using an interval, estimate the average for the dependent variable for a selected value of the independent variable. Interpret this interval. Variable 1 Variable 2 1.85 0.59 Higher 42.98 32.14 Lower 40.78 51.62 MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. 9. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain. We cannot make that prediction Inanatemptoimprovethemodel,useamultipleregresionmodeltopredicthe dependentvariable.Y,basedonaloftheindependentvariables.X1,X2,andX3. Coefficients Intercept 42.41081408 Calls (X1) 0.045278501 Time (X2) -0.388475094 Years (X3) -0.570264816 Y= 58.25874535 11. UsingExcel,runthemultipleregresionanalysisusingthedesignateddependentandthre independentvariables.Statetheequationforthismultipleregresionmodel. Regression Statistics Multiple R 0.332811341 R Square 0.110763389 Adjusted R Square 0.082974745 Standard Error 4.823306161 Observations 100 12. PerformtheGlobalTestforUtility(F-Test).Explaintheconclusion. Itisignificant.ThereisarelationshipacordingtotheANOVAitis0.010080614. ANOVA df SS MS F SignificanceF Regresion 3 278.1888971 92.72963236 3.985922758 0.010080614 Residual 96 2233.371103 23.26428232 Total 99 2511.56 MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. it 13. Performthet-testoneachindependentvariable.Explaintheconclusionsandclearlystatehow theanalysishouldproced.Inparticular,whichindependentvariableshouldbekeptand whichshouldbediscarded.Ifanyindependentvariablesaretobediscarded,re-runthemultiple regresion,includingonlythesignificantindependentvariables,andsummarizeresultswith discusionofanalysis. Decision Rule: Reject Ho if p-value <0.05 WehavetofailtorejectbecausetheNull Hypothesis we don’t have evidence to show there is a relationship between time and sales. Calls are significantly related but time and years are not. 14. Isthismultipleregresionmodelbeterthanthelinearmodelgeneratedinparts1-10?Explain. Thelinearegresionmodelisbeterbecause helpyouunderstandandpredicthebehaviorof dataprovided MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. Test of Slope of Linear Regression n Correlation Coefficient (r) Standard Error of x, sx Standard Error of y, sy Slope (β1) Standard Error (standard deviation) Standard Error of the slope, sb Test Statistic, t Degrees of Freedom Two-Sided p-value One-Sided p-value Confidence Level t Critical Value Confidence Interval For Slope Lower Limit 0.019910 Upper Limit 0.121584 Enter x-value 150 Mean (x) 160.430000 y 41.882109 SSx 36232.51000 0 Standard Error Confidence Interval 0.556028 Standard Error Prediction Interval 4.907834 Confidence Interval for Given x Lower Limit Upper Limit Prediction Interval for Given x Lower Limit Upper Limit 51.621546 32.142672 42.985528 40.778690 100 0.268711 19.130733 5.036794 0.070747 4.876235 0.025617 2.761674 98 0.006867 0.003433 95% 1.984467 MATH 534 Week 7 Course Project Part C: Regression and Correlation Analysis. SUMMARY OUTPUT Regression Statistics Multiple R 0.33281134 1 R Square 0.11076338 9 Adjusted R Square 0.08297474 5 Standard Error 4.82330616 1 Observations 100 ANOVA df SS MS F Significance F Regression 3 278.1888971 92.7296323 6 3.98592275 8 0.010080614 Residual 96 2233.371103 23.2642823 2 Total 99 2511.56 Coefficients Standard Error t Stat P-value Lower 95% Upper 9 Intercept 42.4108140 8 7.811327057 5.42939935 5 4.25114E-07 26.90545242 57.9161 Calls (X1) 0.04527850 1 0.030648312 1.47735710 6 0.14285313 5 - 0.015557917 0.10611 Time (X2) - 0.38847509 4 0.250917312 - 1.54821957 7 0.12485987 9 - 0.886542021 0.10959 Years (X3) - 0.57026481 6 0.393566414 - 1.44896717 7 0.15060543 - 1.351487973 0.21095