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
Imports will exceed 12,000 hectoliters in the year
Using this tool we find the r-value rounded to the thousandths place to be
Check
Type your answer without spaces or commas and rounded to the nearest hundredth.

Answer 1

The linear trend analysis suggests that wine imports in the U.S. are projected to surpass 12,000 hectoliters around the close of 1996, based on the calculated equation.

To determine if the trend is linear, we calculate the slope (m) and y-intercept (b) for the linear equation y = mx + b, where y is the import value, and x is the year.

The slope (m) is calculated using the formula:

m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)

And the y-intercept (b) is calculated using the formula:

b = (Σy - mΣx) / n

After performing the calculations with the provided data, we find that the linear equation is y = 405.75x - 798960.8.

Now, we set y (imports) to 12,000 and solve for x (year):

12000 = 405.75x - 798960.8

405.75x = 810960.8

x ≈ 1996.79

So, according to the linear trend, imports will exceed 12,000 hectoliters around the end of 1996.