Annual Income. The Census Bureau collects data on income by educational attainment, sex, and age. Results are published in Current Population Reports. From a random sample of 75 males between the ages of 25 and 50, all of whom have at least a ninth-grade education, data were collected on age, number of years of school completed, and annual income. We performed a multiple regression analysis for annual income (in thousands of dollars) with the variables age and number of years of school completed as predictor variables. The resulting output is shown in Output A.21. a. Use the computer output to obtain the regression equation for annual income in terms of age and number of years of school completed. b. Apply the regression equation to predict the annual income of a male who is 32 years old and has completed exactly 4 years of college (i.e., 16 years of school). c. Find and interpret the coefficient of determination, R2 d. Find and interpret the standard error of the estimate. e. At the 5% significance level, do the data provide sufficient evidence to conclude that, taken together, age and number of years of school completed are useful for predicting annual income for males (the type of males under consideration)? f. At the 5% significance level, do the data provide sufficient evidence to conclude that age is useful as a predictor of annual income for males? Be precise in your conclusion. g. Repeat part (f) for the predictor variable, number of years of school completed.
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.
Annual Income. The Census Bureau collects data on income by educational attainment, sex, and age. Results are published in Current Population Reports. From a random sample of 75 males between the ages of 25 and 50, all of whom have at least a ninth-grade education, data were collected on age, number of years of school completed, and annual income. We performed a multiple
a. Use the computer output to obtain the regression equation for annual income in terms of age and number of years of school completed.
b. Apply the regression equation to predict the annual income of a male who is 32 years old and has completed exactly 4 years of college (i.e., 16 years of school).
c. Find and interpret the coefficient of determination, R2
d. Find and interpret the standard error of the estimate.
e. At the 5% significance level, do the data provide sufficient evidence to conclude that, taken together, age and number of years of school completed are useful for predicting annual income for males (the type of males under consideration)?
f. At the 5% significance level, do the data provide sufficient evidence to conclude that age is useful as a predictor of annual income for males? Be precise in your conclusion.
g. Repeat part (f) for the predictor variable, number of years of school completed.
Step by step
Solved in 3 steps with 6 images
