Simple Linear Regression Keynes’ Explanation of Consumption
John Maynard Keynes hypothesized that household income was the primary determinant of household spending. To test his theory, 9 regions were selected within the United States based upon average disposable income levels.
The scale income levels for these regions were 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 and 5.0. Per capita household spending was recorded for each region. The results are given in Table 1.
Average Disposable Income Levels 
Per Capita Household Spending 
X 
Y 
.5 
4.21 
1.0 
5.93 
1.5 
7.30 
2.0 
8.32 
2.5 
10.64 
3.0 
11.50 
3.5 
11.80 
4.0 
11.95 
5.0 
11.90 
1. Verify that the least square regression line for predicting consumer spending from income is:
Ÿ = 4.563 + 1.847X
2. Verify that the correlation coefficient between consumer spending and income is 0.9234.
3. The analysis of variance table is of the form:
Source 
Degrees of Freedom 
Sum of Squares 
Mean Squares 
Regression 
1 
58.748 
58.748 
Error 
7 
10.143 
1.449 
Total 
8 
68.891 

Complete the table and test at the significance level that there is a linear regression relation between consumer spending and income. Discuss.
1. What is the percentage of variation in consumer spending that is explained by income?
2. Compute the standard error of the estimated regression line and interpret.
3. Compute the predicted spending when income is 0, 3, 5, and 6 units.
4. Plot the data and comment on the use of the linear model to fit this data.
5. Consider the following data set where Y represents per capita household spending expressed in terms of year 31 dollars and X is disposable income after taxes.
Year 
Disposable Income X 
Household Spending Y 


27 
3319 
3042 
28 
3421 
3124 
29 
3404 
3108 
30 
3276 
2994 
31 
3271 
2971 
The predictor equation using all 31 data points is:
Ycircumflex = 227 + 0.98X
a. What would be the effect upon consumer spending if Congress introduces a tax cut in year 32 that increases per capita disposable income by $100?
b. How would consumer spending in year 32 been effected by a tax increase that would have lowered per capita disposable income by $100?