Compare homoscedasticity with heteroscedasticity? Illustrate with suitable diagrams. What are the consequences of heteroscedasticity in a bivariate linear regression model?
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- What is regression analysis? Describe the process of performing regression analysis on a graphing utility.The following result perspective in RapidMiner shows a multiple linear regression model. Based on the diagram, the model for our dependent variable Y is Predicted Y= (Insulation *0.420)+(Temperature *0.071)+(Avg_Age*0.065)+(Home_Size *0.311)+7.589 Attribute Insulation Temperature Avg Age Home Size (Intercept) O True O False Coefficient 3.323 -0.869 1.968 3.173 134.511 Std. Error 0.420 0.071 0.065 0.311 7.589 Std. Coefficient 0.164 -0.262 0.527 0.131 ? Tolerance 0.431 0.405 0.491 0.914 ? t-Stat 7.906 -12.222 30.217 10.210 17.725Provide an example of a regression that arguably would have a high value of R² but would produce biased and inconsistent estimators of a causal effect. Explain why the R² is likely to be high. Explain why the OLS estimators would be biased and inconsistent.
- Explain why all-subsets regression is considered superior to stepwise regression in selecting a regression equation.Explain Heteroskedasticity and Autocorrelation Standard Errors for regression?What are some examples of ways in which linear regression to create a beneficial statistical outcome, in a business setting?
- Does correcting the sugar cane model for heteroscedasticity improve its performance? Interpret the regression coefficients.Which is NOT true of simple linear regression? It can be used to identify predictors of continuous outcome variables. It can be used to predict the outcome of a binary variable (e.g., pass/fail) with continuous variables. It can be used to quantify a relationship between two continuous variables. It can be used to model a linear relationship between variables.What characteristics are associated with serum Glucose? Use simple and multivariable linear regression analysis to complete the following table relating the characteristics listed to Glucose as a continuous variable. Before conducting the analysis, be sure that all participants have complete data on all analysis variables. If participants are excluded due to missing data, the numbers excluded should be reported. Then, describe how each characteristic is related to Glucose level. Are crude and multivariable effects similar? What might explain or account for any differences? Outcome Variable: Glucose mg/dL Characteristic Regression Coefficient Crude Models p-value Regression Coefficient Multivariable Model p-value Age, years 32-81 Male sex 1=male 2=female Systolic blood pressure, mmHg 83-295 Total serum cholesterol, mg/dL 107-696 Current smoker 0=no 1=yes Diabetes 0=no…
- A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in meter square and income is measured in IDR millions. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Which of the independent variables in the model are significant at the 5% level? Formulate the hypothesis and explain the answer. How far can you rely upon this model? Or, what is the percentage variation in House explained by the model? What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of IDR 400 million and having a family size of 4?Issue of multicollinearity impacted the ‘validity and trustworthiness’ of a regression model. Demonstrate how this issue can be a problem by using appropriate hypothetical example.(INCLUDE TABLE AND FIGURES)What is the interpretation of the coefficient of determination in a simple linear regression model?