Byers_eab_703_psc10

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University of Nevada, Las Vegas *

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703

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Statistics

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Jan 9, 2024

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docx

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3

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EAB 703 Problem Set c10 Madison Byers NOTE: Assume we are testing at α = 0.05 for all statistical tests The data for this problem were collected on a simple random sample of 20 patients with hypertension. [ DATA: eab_703_psc10 ] This is the same study as for the Chapter 9 problem set, but with more variables.
Now, include all of the variables in a multiple regression equation to predict blood pressure. What is the final mathematical representation of the model including all variables? Regression Statistics Multiple R 0.998073271 R Square 0.996150254 Adjusted R Square 0.996150254 Standard Error 0.407228696 Observations 20 ANOVA df SS MS F Significance F Regression 6 557.8441423 99.97402 560.641 6.39523E-15 Residual 13 2.155857737 0.165835 Total 19 560 Coefficients Standard Error t-stat P-value Intercept -12.87047602 2.556649879 -5.03412 0.000229 X1 0.703259394 0.049605805 14.17696 2.76E-09 X2 0.969919778 0.063108457 15.36909 1.02E-09 X3 3.776491003 1.580150865 2.389956 0.032694 X4 0.06838304 0.04844149 1.411663 0.181534 X5 -0.084484687 0.05160898 -1.63702 0.125594 X6 0.0055715 0.0034123 1.63277 0.126491 The regression model is: y= -12.87 + 0.703 x1 + 0.970 x2 + 3.777 X3 + 0.068 x4 - 0.085 x5 + 0.006 x6
Next, use the techniques of this chapter to develop what you believe is the most appropriate model (this could be one with fewer variables). Write your final model below and explain why you have retained or excluded each of the variables. Regression Statistics Multiple R 0.99726756 8 R Square 0.99454260 3 Adjusted R Square 0.99351934 1 Standard Error 0.43704563 8 Observations 20 ANOVA df SS MS F Significance F Regression 3 556.9438578 185.64795 971.9336 2.62045E-18 Residual 16 3.056142238 0.1910089 Total 19 560 Coefficients Standard Error t-stat P-value Intercept -13.667 2.647 -5.164 9.42E-05 X1 0.702 0.044 15.961 3E-11 X2 0.906 0.049 18.490 3.2E-12 X3 4.627 1.521 3.042 0.007764 New model is: y= -13.667 + 0.702 x1 + 0.906 x2 + 4.627 x3 Decision rule: If P-value < 0.05, then variable is statistically significant. and if P-value > 0.05, then variable is not significant.
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