Question

Question

The accompanying table shows wind speed and the corresponding wind chill factor when the air
temperature is 24°F. Write a logarithmic regression equation for this set of data, rounding all coefficients
to the nearest ten-thousandth. Using this equation, find the wind chill factor, to the nearest degree, when
the wind speed is 20 miles per hour.
Wind Speed in MPH (x) Wind Chill in °F (y)
1
23
17
16
13
11
9
3
Show Examples
4
6
9
12

Answer 1

Answer:we get the following logarithmic regression equation, rounding all coefficients to the nearest ten-thousandth:

y = 23.9003 - 1.1769 * ln(x)

Using this equation, we can find the wind chill factor, to the nearest degree, when the wind speed is 20 miles per hour by plugging in x = 20 and rounding the result:

y = 23.9003 - 1.1769 * ln(20) y = 23.9003 - 1.1769 * 2.9957 y = 23.9003 - 3.5275 y = 20.3728

Rounding to the nearest degree, we get y = 20.

Therefore, the wind chill factor when the wind speed is 20 miles per hour is 20°F.

Answer 2

Answer: 23.8°F

Explanation:

To find the logarithmic regression equation for wind speed and wind chill factor when the air temperature is 24°F, we can use the formula:

y = m*log(x) + b

where y is the wind chill factor, x is the wind speed in mph, m is the slope of the line, log(x) is the logarithm of x, and b is the intercept.

First, we need to find the slope and intercept of the line. We can do this by using some pairs of x and y values from the table. For example, if we use the points (1, 23) and (3, 9), we can find the slope and intercept using the formulas:

m = (y2 - y1)/(x2 - x1)

b = y1 - m*x1

Plugging in the values, we get:

m = (9 - 23)/(3 - 1) = -14/2 = -7

b = 4 - (-7) * 3 = 23 - 21 = 2

So the logarithmic regression equation for wind speed and wind chill factor when the air temperature is 24°F is:

y = -7*log(x) + 2

To find the wind chill factor when the wind speed is 20 miles per hour, we can substitute 20 for x in the equation:

y = -7*log(20) + 2

y = 23.8

So the wind chill factor when the wind speed is 20 miles per hour is approximately 23.8°F.