Calculate correlation coefficient r to show the relationship between number of farms and average size of the farms. Interpret your findings. Year Number of Farms (millions) Average Size (acres) 1950 5.65 213 1955 4.65 258 1960 3.96 297 1965 3.36 340 1970 2.95 374 1975 2.52 420 1980 2.44 426 1985 2.29 441 1990 2.15 400 1995 2.07 469 2000 2.17 434 2005 2.10 444
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Number of Farms: [5.65, 4.65, 3.96, 3.36, 2.95, 2.52, 2.44, 2.29, 2.15, 2.07, 2.17, 2.10] Average Size: [213, 258, 297, 340, 374, 420, 426, 441, 400, 469, 434, 444] Show more…
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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 Number of Farms (millions) Average Size (acres) 1960 5.69 218 1965 4.70 260 1970 3.91 298 1975 3.32 342 1980 2.95 372 1985 2.52 419 1990 2.47 426 1995 2.31 446 2000 2.16 459 2005 2.07 472 2010 2.18 433 2015 2.10 443 (Do not round the intermediate values. Round your answers to 2 decimal places.) y^= ______ +( _____ )x
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SIZE OF U.S. FARMS Use the data in the table below to make a line graph showing the average acreage of U.S. farms for selected years from 1950 through 2007 . $$\begin{array}{l|cc}\hline & \text { Number of } & \text { Average size } \\\text { U.S.farms } & \text { of U.S. farms } \\\text { Year } & \text { (in millions) } & \text { (acres) } \\\hline 1950 & 5.6 & 213 \\1960 & 4.0 & 297 \\1970 & 2.9 & 374 \\1980 & 2.4 & 426 \\1990 & 2.1 & 460 \\2000 & 2.2 & 436 \\2007 & 2.1 & 449 \end{array}$$
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The table shows the acres x of corn planted and acres y of corn harvested, in millions of acres, in a particular country in ten successive years. x | 75.7 78.9 78.6 80.9 81.8 y | 68.8 69.3 70.9 73.6 75.1 x | 78.3 93.5 85.9 86.4 88.2 y | 70.6 86.5 78.6 79.5 81.4 Compute the linear correlation coefficient for these sample data and interpret its meaning in the context of the problem.
Supreeta N.
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