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Part 3. Multivariate Linear Regression & Confounding Variables Confounding variables are a third variable that influences both the independent variable and dependent variable, causing a spurious association. We control for confounding variables by including them in our multivariate regression models, which removes their effects from the association between X and Y. 29. When considering the association between height and weight, what potential confounding variable (included in this dataset) should we adjust for? Why? 30. What is another potential confounding variable (not included in this dataset)? Why? Run a multivariate regression model using Weight as the Dependent Variable. Transfer Height and the confounding variable we do have data on (#29 above) to the Covariates box. 31. Is Height still a significant predictor of Weight when adjusting for this confounding variable? How can you tell? 32. Write the results of this multivariate linear regression in APA format. DE CELL Casus
Dependent Variable Weight Method Enter Covariates. Waist BMI Factors WLS Weights (optional) change ves partial correlations ty diagnostics Model Summary - Weight Model R R² 0.000 0.000 0.859 0.738 Sum of Squares F Mean Square H₁ 36999.455 2 59.293 Regression Residual 18499.728 312.004 13104.170 42 Total 50103.626 44 Note. The intercept model is omitted, as no meaningful information can be shown. Coefficients Model Unstandardized Standard Error Standardized t 163.682 5.030 32.539 -27.411 19.402 -1.413 1.656 0.228 0.727 7.274 1.708 0.879 0.194 1.943 ... H₂ H₁ ANOVA Model H₂ H₂ Descriptives Weight Waist BMI (Intercept) (Intercept) Waist BMI N 45 45 45 Adjusted R² 0.000 0.726 Mean SD 163.682 33.745 88.207 14.804 26.349 3.834 df RMSE 33.745 17.664 SE 5.030 2.207 0.572 P <.001 Р <.001 0.165 <.001 0.059
Spearman's Correlations Variable 1. Waist n Spearman's rho p-value 2. Weight n Spearman's rho p-value 3. ID# n Spearman's rho p-value n Spearman's rho p-value n Spearman's rho p-value n Spearman's rho p-value n Spearman's rho p-value Waist Weight 45 0.866 < .001 45 -0.004 0.980 45 0.540 <.001 5. Height 45 0.463 0.001 6. Pulse 45 0.151 0.322 7. BMI 45 0.672 < .001 Assumption checks Shapiro-Wilk Test for Multivariate Normality Shapiro-Wilk Р < .001 4. Age 0.690 IIT 45 -0.148 0.333 45 0.401 0.006 45 0.631 <.001 45 0.255 0.091 45 0.671 <.001 ID# 1114 45 1.977e-41 0.999 45 -0.138 0.367 45 -0.360 0.015 45 -0.108 0.481 Age 111 45 0.406 0.006 45 -0.092 0.550 45 0.080 0.600 Height III 45 0.116 0.448 45 0.118 0.441 Pulse 111 45 0.452 0.002 BMI 111
Descriptives under Statistics. 12. What is the null hypothesis in words? There is no significant association between the height and weight. 13. What is the null hypothesis in symbols? B1 = 0 14. What is the alternative hypothesis in words? There is a significant association between the height weight. 15. What is the alternative hypothesis in symbols? B1 #0 GRA 16. What is your sample size (n)? 45 17. What is the slope? 2.15 (This means as height increases 1 inch, weight increases 2.15 lbs.) 18. What is the y-intefcept? 24.33 (This is the weight predicted [Y] if height [X] equals O.) 19. What percent of the variance il weight does height account for (R2)? 48.5% 20. What is the equation for this analysis? Weight = 2.15x+24.33 le can use the linear regression equation to make predictions for X- and Y-values. 21. For someone who is 66" what is their predicted weight? 166.23 lbs. 22. For someone who is 120lbs what is their predicted height? 44.50 inches un another linear regression using Weight as the Dependent Variable and Waist as the Covariate. 23. What is the slope? 1.93 24. As waist circumference increases 1 cm, weight increases 1.93 lbs. 25. What is the y-intercept? -6.32 26. What proportion of variance in weight does waist size account for? 71.5% 27. Write the regression equation for this analysis. Weight = 1.93x* Waist + (-6.32) 28. For someone with a waist circumference of 100cm, what is their predicted weight? 186.68 lbs.