Eleven states were randomly selected from among the 50 United States. This data represents the percentage of households in each state that are below the poverty level (Poverty Rate) based on household income and the percentage of adults in the state who had earned at least a high school degree (HS and Above). (a) Describe the relationship between the variables. (b) What is the slope of the least-squares regression line for this data? Interpret this value. (c) Predict the percent of adults who had attained at least a high school degree for the state with a poverty rate of 15%? Show your work. (d) Find the residual for the state with a poverty rate of 15%. Interpret the residual.
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.
Eleven states were randomly selected from among the 50 United States. This data represents the percentage of households in each state that are below the poverty level (Poverty Rate) based on household income and the percentage of adults in the state who had earned at least a high school degree (HS and Above).
(a) Describe the relationship between the variables.
(b) What is the slope of the least-squares regression line for this data? Interpret this value.
(c) Predict the percent of adults who had attained at least a high school degree for the state with a poverty rate of 15%? Show your work.
(d) Find the residual for the state with a poverty rate of 15%. Interpret the residual.
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