Question
In: Statistics and Probability
It appears that over the past 50 years, the number of farms in the United States...
It appears that over the past 50 years, the number of farms in the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Use these data to develop the equation of a regression line to predict the average size of a farm by the number of farms Discuss the slope and y-intercept of the model. Year Number of Farms (millions) Average Size (acres) 1950 5.70 209 1955 4.63 262 1960 3.91 296 1965 3.35 336 1970 2.95 374 1975 2.51 421 1980 2.45 425 1985 2.32 441 1990 2.15 459 1995 2.07 469 2000 2.17 433 2005 2.11 444 2010 2.19 420
Solutions
Expert Solution
(a)
From the given data, the following Table is calculated:
| X | Y | XY | X2 |
| 5.70 | 209 | 1191.3 | 32.49 |
| 4.63 | 262 | 1213.06 | 21.4369 |
| 3.91 | 296 | 1157.36 | 15.2881 |
| 3.35 | 336 | 1125.6 | 11.2225 |
| 2.95 | 374 | 1103.3 | 8.7025 |
| 2.51 | 421 | 1056.71 | 6.3001 |
| 2.45 | 425 | 1041.25 | 6.0025 |
| 2.32 | 441 | 1023.12 | 5.3824 |
| 2.15 | 459 | 986.85 | 4.6225 |
| 2.07 | 469 | 970.83 | 4.2649 |
| 2.17 | 433 | 939.61 | 4.7089 |
| 2.11 | 444 | 936.84 | 4.4521 |
| 2.19 | 420 | 919.8 | 4.7961 |
| Total = 38.51 | 4989 | 13665.63 | 129.6895 |
So,
Equation of Regression Line is:
y = 595.03 - 71.316 x
(b)
Slope = - 71.316. For every increase of 1 number of farm, there is decrease of 71.316 in the average size of a farm.
y - intercept = 595.03 is the average size of a farm for no farm at all and so in this case the y intercept is meaningless.
orchestra answered 1 year agoRelated Solutions
It appears that over the past 50 years, the number of farms in the United States...
It appears that over the past 50 years, the number of farms in
the United States declined while the average size of farms
increased. The following data provided by the U.S. Department of
Agriculture show five-year interval data for U.S. farms. Use these
data to develop the equation of a regression line to predict the
average size of a farm (y) by the number of farms (x). Discuss the
slope and y-intercept of the model.
Year
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It appears that over the past 50 years, the number of farms in the United States...
It appears that over the past 50 years, the number of farms in
the United States declined while the average size of farms
increased. The following data provided by the U.S. Department of
Agriculture show five-year interval data for U.S. farms. Use these
data to develop the equation of a regression line to predict the
average size of a farm (y) by the number of farms (x). Discuss the
slope and y-intercept of the model.
Year
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Exponential
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Click here for the Excel Data File
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