Question

The ordered pairs show amounts y​ (in inches) of rainfall equivalent to x​ inches of snow.(16, 1.5), (12, 1.3), (18, 1.8), (15, 1.5), (20, 2.1),(23, 2.4)​ About how many inches of rainfall are equivalent to 6 inches of snow? Round your answer to the nearest hundredth, if necessary.

Answer 1

Answer:

0.57 inches of rainfall is equivalent to 6 inches of snow

Step-by-step explanation:

The given data are presented here as follows;

$\begin{array}{cc}x&y\\16&1.5\\12&1.3\\18&1.8\\15&1.5\\20&2.1\\23&2.4\\\end{array}$

The data points are approximately linear

From the the trend line of the plotted points of the graph, created with Microsoft Excel, with Forecasting, when there is 6 inches of snow the rainfall is 0.575 inches

By linear regression, we have;

Y = a + b·X

Where;

$b = \dfrac{n \cdot \sum XY - \left (\sum X \right ) \cdot \left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}$

$a = \dfrac{\sum Y - b \cdot \sum X}{n}$

∑x = 104

∑y = 10.6

∑(x·y) = 191.7

(∑x)·(∑y) = 1102.4

(∑x)² = 10816

n = 6

SigX^2 = 1878

Plugging in the values, gives;

$b = \dfrac{6 \times191.7 - 1102.4}{6 \times 1878 - 10816} \approx 0.10575$

$a = \dfrac{10.6 - 0.10575 \times 104}{6} \approx -0.06637$

Therefore;

Y = 0.10575·x - 0.06637

When x = 6 inches, we have;

Y = 0.10575 × 6 - 0.06637 = 0.56813

Y = 0.56813 inches ≈ 0.57 inches of rainfall

Therefore;

0.57 inches of rainfall is equivalent to 6 inches of snow