Complete the table below by finding the product of each x-value times its corresponding y-value. For example, if x1 = 5 and y1 = 10, then x1y1 = (5)(10) = 50. Write these in the last column and calculate the sum of these xy values in the bottom row. Temperature (°C) x Solubility (g/100mL) y x2 y2 xy 10 31 20 33 30 37 40 41 50 42 Sums: Next, you need to find the square of the sum of the x-values (∑x)2 and the square of the sum of the y-values (∑y)2. Note that these are different from the sums of the squared x-values (∑x2) and the sums of squared y-values (∑y2). If the x-values are 3, 5, 6 then the sum of the x-values is ∑x = 3+5+6 = 14, the square of the sum of the x-values is (∑x)2 = (14)2 = 196, and the sum of the squared values 9, 25, 36 is ∑x2 = 9+25+36 = 70. Calculate the square of the sum of the x-values and the square of the sum of the y-values and enter these two sums below: (∑x)2 = (∑y)2 = To help keep things organized for the remaining calculations, rewrite the values you've calculated from the previous questions into the appropriate blanks below: ∑x = ∑y = ∑x2 = ∑y2 = ∑xy = (∑x)2 = (∑y)2 = n = number of (xi,yi) data pairs =
Complete the table below by finding the product of each x-value times its corresponding y-value. For example, if x1 = 5 and y1 = 10, then x1y1 = (5)(10) = 50. Write these in the last column and calculate the sum of these xy values in the bottom row.
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Temperature (°C) x |
Solubility (g/100mL) y |
x2 |
y2 |
xy |
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10 |
31 |
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20 |
33 |
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30 |
37 |
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40 |
41 |
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50 |
42 |
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Sums: |
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Next, you need to find the square of the sum of the x-values (∑x)2 and the square of the sum of the y-values (∑y)2. Note that these are different from the sums of the squared x-values (∑x2) and the sums of squared y-values (∑y2). If the x-values are 3, 5, 6 then the sum of the x-values is ∑x = 3+5+6 = 14, the square of the sum of the x-values is (∑x)2 = (14)2 = 196, and the sum of the squared values 9, 25, 36 is ∑x2 = 9+25+36 = 70.
Calculate the square of the sum of the x-values and the square of the sum of the y-values and enter these two sums below:
(∑x)2 =
(∑y)2 =
To help keep things organized for the remaining calculations, rewrite the values you've calculated from the previous questions into the appropriate blanks below:
∑x =
∑y =
∑x2 =
∑y2 =
∑xy =
(∑x)2 =
(∑y)2 =
n = number of (xi,yi) data pairs =
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