Question

The U.S. import of wine (in hectoliters) for several years is given in the table below. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters? Year Imports 1992 2665 1994 2688 1996 3565 1998 4129 2000 4584 2002 5655 2004 6549 2006 7950 2008 8487 2009 9462 Using this tool we find the linear regression line to be y=Answer Type your answer without spaces or commas and rounded to the nearest hundredth. Imports will exceed 12,000 hectoliters in the year Answer Using this tool we find the r-value rounded to the thousandths place to be Answer

Answer 1

After plotting the U.S. wine imports data on a graph and applying linear regression analysis, we use the equation of the line to calculate the year when imports will exceed 12,000 hectoliters.

To determine if the trend of wine imports is linear and predict when the imports will exceed 12,000 hectoliters, we can use the given data to construct a linear regression. By plotting the import amounts against the years and using a linear regression tool, we find the equation of the best fit line. Assuming the provided data follows a linear trend and the equation you found is y = mx + b where m is the slope and b is the y-intercept, you can calculate when the import level will surpass 12,000 hectoliters.

To do this calculation:

Set y (the import amount) to 12,000.

Solve the equation for x (year) using the formula x = (y - b)/m.

Round your answer to the nearest whole number to find the year.

The linear regression's r-value indicates how closely the data fits the linear model, with values closer to 1 representing a stronger linear relationship. To find the r-value, you would typically use a calculator or software that provides regression analysis.