Exercise 16.037
{Exercise 16.37} The following exercises require the use of a
computer and software. Dataset:
An economist for the federal government is attempting to produce a better measure of poverty than is currently in use. To help acquire information, she recorded the annual household income (in $1,000s) and the amount of money spent on food during one week for a random sample of households. a) Determine the coefficient of determination
(to 4 decimals) and describe what it tells you. b) ______% of the variation in food budgets is explained by the variation in household income. c) Conduct a test to determine
whether there is evidence of a linear relationship between
household income and food budget. |
Regression output using Excel
Regression Statistics | ||||||
Multiple R | 0.495853374 | |||||
R Square | 0.245870569 | |||||
Adjusted R Square | 0.2407751 | |||||
Standard Error | 36.93932351 | |||||
Observations | 150 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 65841.58033 | 65841.58 | 48.2528 | 1.1E-10 | |
Residual | 148 | 201948.016 | 1364.514 | |||
Total | 149 | 267789.5963 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | 153.8985946 | 17.01994055 | 9.042252 | 7.9E-16 | 120.2651 | 187.5321 |
Income | 1.95820496 | 0.281901224 | 6.946422 | 1.1E-10 | 1.401134 | 2.515276 |
Therefore ,Answers
(a) R^2 = 0 .2459
( b ) 24 .59 %
( c ) is
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