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22/08/2022
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:
Y-circumflex = -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?
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