Question

Section 6.2 The apparent temperature or he it feels despite what the thermometer says. The more moisture that is in the air the hotter it will feel. The chart shows the heat index for a temperature of 90° as a function of humidity. at index is a measure of how hot 3. Humidity (%) Heat index ( FO) 91 93 95 97 100 103 105 109 45 Use regression to find a quadratic equation to model the data. Round the numbers in your equation to 4 decimal places. Use your equation to predict the heat index at 85% humidity. a) 65 70 75 b) 113 Heat Index (at 90°) Based on Humidity 2 105 100 E 90 30 40 50 60 70 80 90 Humidity (percent)

Answer 1

(a)

Step 1 -

In first step, we simply draw the graph and use Excel to find quadratic regression equation. Here is the screenshot is attached -

Humidity (%) Heat Index (FO) 91 93 95 97 100 103 105 109 113 Heat Index (FO) based on Humidity 45 115 110 y 0.0055x, 0.1145x + 86.994 105 70 75 100 95 90 85 30 50 Humidity (%)

Step 2 - Hence by using regression quadratic line which is obtained by Excel graph -

y 0.0055x2-0. 1 145x 86.994

where y is Heat Index and x is Humidity (%).

(b)

Step 3 - for Humidity 85% -

$x=85$

y = 0.0055 (85) 2-0, 1 145(85) + 86.994

y = 39.7375-9.7325+ 86.994

y= 116.9998 117

Hence Heat Index would be 117 for 85% Humidity.