Question

10.2.22 : Question Help The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 1240 1195 928 809 932 763 Temperature (°F) 95.2 85.5 77.5 67.8 72.5 66.7 What is the regression equation? y= + x (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.)

Answer 1

Solution-

• 
  The following data are passed: Bug chirps per minute Temperature (°F) 1240 95.2 1195 85.5 928 77.5 809 67.8 932 72.5 763 66.7 The independent variable is Bugchirpsperminute, and the dependent variable is Temperature(°F). In order to compute the regression coefficients, the following table needs to be used: Bug chirps per minute Temper ature (°F) Bug chirps per minute* Temper ature (°F) Bug chirps per minute? Temper ature (°F)2 153760 1240 95.2 118048 9063.04 102172 142802 1195 85.5 7310.25 928 77.5 71920 861184 6006.25 809 67.8 54850.2 654481 4596.84 932 72.5 67570 868624 5256.25 763 66.7 50892.1 582169 4448.89 465452. 593208 36681.5 Sum = 5867 465.2
  
  Based on the above table, the following is calculated: 8 = 3x3 = 5867 – 97.83333333 = 3Y, 465,2 = 7.523333333 586x = x - : (Ex.) 590208 – 5807'/6 = 1065134583 8 SSyy = ☺ 554 = xy-- (2x) () – 4054325 – 5867 40526 – 10 Y- - Y = 36681.52 - 465.22 /6 = 613.01333333334 SSXY =) - X D Y = 465452.8 - 5867 x 465.2/6 = 10- n 1 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows: SSXY SSxx 10564.733333333 195134.83333333 = 0.0541 n=Y-X. m = 77.533333333333 - 977.83333333333 < 0.0541 = 24.5928 Therefore, we find that the regression equation is: Temperature(°F) = 24.5928 +0.0541Bugchirpsperminute Graphically: Regression of Bug chirps and Tenperature Tenperature (°F) 687.60717.60767.60817.60867.60917.60967.60017.60067.60117.60167.60217.61267.60317.60 Ruin whirps per ninute - Regression equation: Y = 24.5928 + 0.0541 * X
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• The regression equation is

y` = 24.59 + (0.0541) x

• Predicted Temperature when bug chirping = 3000

y` = 24.59 + (0.0541) × (3000)

y` = 186.89

above predicted value is outside of the interval of Temperature average values.