How much does household weekly income affect the household weekly expenditure on food? | ||||||||
The following data shows household weekly expenditure on food and the household weekly income (all in dollars). |
Use the data below to develop an estimated regression equation that could be used to predict food expenditure for a weekly income. |
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Use Excel commands for your calculations. |
FOOD |
INCOME |
y |
x |
91 |
292 |
148 |
479 |
107 |
428 |
146 |
766 |
243 |
1621 |
312 |
1661 |
243 |
1292 |
272 |
1683 |
349 |
1808 |
223 |
1147 |
205 |
1648 |
182 |
1351 |
414 |
1919 |
291 |
2046 |
212 |
1577 |
298 |
1805 |
374 |
2031 |
141 |
1618 |
205 |
1999 |
387 |
1953 |
426 |
2114 |
136 |
1606 |
273 |
1833 |
400 |
2166 |
192 |
2124 |
25 |
The margin of error for a 95% confidence interval for the population slope parameter is, |
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a |
0.0721 |
7.2 |
¢ |
||
b |
0.0627 |
6.3 |
¢ |
||
c |
0.0545 |
5.5 |
¢ |
||
d |
0.0463 |
4.6 |
¢ |
||
26 |
The upper boundary of the 95% interval estimate for β₁ is, |
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a |
0.1870 |
18.7 |
¢ |
||
b |
0.1795 |
18.0 |
¢ |
||
c |
0.1687 |
16.9 |
¢ |
||
d |
0.1552 |
15.5 |
¢ |
||
27 |
The value of the test statistic to test the hypothesis that weekly income has no impact on food expenditure is, |
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a |
6.030 |
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b |
5.025 |
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c |
4.020 |
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d |
3.216 |
from excel: data-data analysis:regression :below is the output for slope:
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 44.36508 | 43.42596 | 1.021626 | 0.317584 | -45.4684 | 134.1985 | -45.4684 | 134.1985 |
x | 0.132442 | 0.026355 | 5.025345 | 4.38E-05 | 0.077923 | 0.186961 | 0.077923 | 0.186961 |
25)
margin of error for a 95% confidence interval =(upper limit-lower limit)/2=0.0545
26) upper boundary of the 95% interval estimate for β =0.1870
27)
value of the test statistic =5.025
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