An economist is studying the relationship between income and savings. He has randomly selected seven subjects and obtained income and savings data from them. He wishes to use a simple linear regression model to predict savings based on annual income. Income and Savings
Income (Thousands of Dollars) 28 ,25 ,34 ,43 ,39 74
Savings (Thousands of Dollars) 0.2 ,0 ,0.8, 1.2 ,3.1 ,2.1 ,8.3
a. What level of measurement do the two variables in the table possess?
b. Which of the variables is the dependent variable in the model?
c. Which of the variables is the independent variable in the model?
d. Draw a scatterplot of the data. Does the scatterplot suggest that a linear model is appropriate? Explain.
e. Use the data to estimate the appropriate model.
f. Predict the savings for someone who earns fifty thousand dollars annually.
g. Interpret the meaning of the slope coefficient in the problem.
h. What fraction of the variation in savings is explained by income?