Question

The store Clothes-4-You keeps data on their sales. These data points represent their coat sales, where x is the average outside temperature and y is the number of coats sold.

(3, 94), (12, 91), (16, 83), (21, 93), (27, 82), (29, 69), (40, 71), (43, 63), (60, 38), (52, 53)

What is the best estimate for the number of coats sold when the outside temperature is 35°F?

Answer 1

To estimate the number of coats sold when the outside temperature is 35°F, we can use linear interpolation based on the existing data points. The given points are:

- (29, 69): 29°F leads to 69 coats sold
- (40, 71): 40°F leads to 71 coats sold

Since 35°F is between 29°F and 40°F, we will perform linear interpolation between these two points.

The formula for linear interpolation is:

\[
y = y_1 + \left( \frac{y_2 - y_1}{x_2 - x_1} \right)(x - x_1)
\]

Where:
- \((x_1, y_1)\) is the first point (29, 69)
- \((x_2, y_2)\) is the second point (40, 71)
- \(x\) is the temperature for which we want to estimate the number of coats sold (35°F)

Substituting the values into the formula:

- \(x_1 = 29\)
- \(y_1 = 69\)
- \(x_2 = 40\)
- \(y_2 = 71\)
- \(x = 35\)

Now substituting in:

\[
y = 69 + \left( \frac{71 - 69}{40 - 29} \right)(35 - 29)
\]
\[
y = 69 + \left( \frac{2}{11} \right)(6)
\]
\[
y = 69 + \frac{12}{11}
\]
\[
y = 69 + 1.09 \approx 70.09
\]

Therefore, the best estimate for the number of coats sold when the outside temperature is 35°F is approximately **70 coats**.