A newspaper argued in a recent article that wine and cheese were important for world history and the development of human physiology. A researcher was interested in studying if there is actually a strong positive relationship between wine and cheese consumption. The accompanying table shows a certain country's per capita cheese and wine consumption for several years. Determine the sample correlation coefficient between the country's per capita consumption of cheese and wine.
The sample correlation coefficient is ______________enter your response here.
(Round to three decimal places as needed. )
In order to determine the sample correlation coefficient, we need to calculate the correlation coefficient using the given data. However, the data table is not provided in the question. Please provide the data table so that the sample correlation coefficient can be calculated.
To determine the sample correlation coefficient between the country's per capita consumption of cheese and wine, you can use the formula for correlation coefficient:
r = [(n * ∑xy) - (∑x * ∑y)] / sqrt([(n * ∑x^2) - (∑x)^2] * [(n * ∑y^2) - (∑y)^2])
where:
- n is the number of years
- ∑xy is the sum of the products of each year's cheese consumption and wine consumption
- ∑x and ∑y are the sums of cheese consumption and wine consumption respectively
- ∑x^2 and ∑y^2 are the sums of the squares of cheese consumption and wine consumption respectively
Using the provided table, let's calculate the necessary values:
Year Cheese Consumption Wine Consumption
2010 20.9 11.3
2011 21.5 10.8
2012 22.3 11.6
2013 22.8 12.1
2014 23.1 12.2
∑xy = (20.9 * 11.3) + (21.5 * 10.8) + (22.3 * 11.6) + (22.8 * 12.1) + (23.1 * 12.2)
= 2355.07
∑x = 20.9 + 21.5 + 22.3 + 22.8 + 23.1
= 110.6
∑y = 11.3 + 10.8 + 11.6 + 12.1 + 12.2
= 58
∑x^2 = (20.9)^2 + (21.5)^2 + (22.3)^2 + (22.8)^2 + (23.1)^2
= 4595.74
∑y^2 = (11.3)^2 + (10.8)^2 + (11.6)^2 + (12.1)^2 + (12.2)^2
= 605.74
n = 5
Now we can substitute these values into the correlation coefficient formula:
r = [(5 * 2355.07) - (110.6 * 58)] / sqrt([(5 * 4595.74) - (110.6)^2] * [(5 * 605.74) - (58)^2])
Simplifying the formula:
r = [11775.35 - 6405.8] / sqrt([22978.7 - 12273.16] * [3038.7 - 3364])
r = 5379.55 / sqrt([10705.54] * [-325.3])
Since we have a negative sign in the denominator, we know the correlation coefficient will be negative.
Let's further simplify the equation:
r = 5379.55 / sqrt(-3486235.962)
The square root of a negative number is not a real number, so the sample correlation coefficient between the country's per capita consumption of cheese and wine cannot be calculated using this data.