Please answer both multiple choice questions below. a.) A linear regression of age (x) on blood lead levels (y) is performed in a sample of men who have worked in factories that manufacture car batteries. The residual plots suggest there is still a pattern remaining, and you decide to add a cubic term for age into the model. Which of the following models is now most appropriate? Blood lead levels = α+ β21(age) + ε, ε ~iid N(0, σ2) Blood lead levels = α+ β1(age3) + ε2, ε ~ iid N(0, σ2) Blood lead levels = α+ β1(age) + β2 (age2) + ε, ε ~iid N(0, σ2) Blood lead levels = α+ β1(age) + β2 (age2) + β1 (age3) + ε, ε ~iid N(0, σ2) b.) A study has been conducted to analyze the sensitivity and specificity of a screening test. If the area under the ROC curve is 1: The screening test is very helpful. The screening test is not helpful. The screening test is somewhat helpful. Helpfulness cannot be determined from the information given.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Please answer both multiple choice questions below.
a.) A linear regression of age (x) on blood lead levels (y) is performed in a sample of men who have worked in factories that manufacture car batteries. The residual plots suggest there is still a pattern remaining, and you decide to add a cubic term for age into the model. Which of the following models is now most appropriate?
- Blood lead levels = α+ β21(age) + ε, ε ~iid N(0, σ2)
- Blood lead levels = α+ β1(age3) + ε2, ε ~ iid N(0, σ2)
- Blood lead levels = α+ β1(age) + β2 (age2) + ε, ε ~iid N(0, σ2)
- Blood lead levels = α+ β1(age) + β2 (age2) + β1 (age3) + ε, ε ~iid N(0, σ2)
b.) A study has been conducted to analyze the sensitivity and specificity of a screening test. If the area under the ROC curve is 1:
- The screening test is very helpful.
- The screening test is not helpful.
- The screening test is somewhat helpful.
- Helpfulness cannot be determined from the information given.
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