Question

The common cricket can be used as a crude thermometer. The colder the temperature, the slower the rate of chirping. The table below shows the average chirp rate of a cricket at various temperatures.

Chirp Rate
(chirps/sec)    Temperature (F)
2.4   61.9
3.8   83.6
3.7   71.8
2.0   47
3.4   65.1
3.9   75.8

Find the correlation coefficient for the data. Round to three decimal places

Find the least-squares regression line equation for predicting the temperature, y, from the chirp rate, x. Choose the correct answer.

a) y = -0.683 + 0.057x
b) y = 0.057 - 0.683x
c) y = 14.354 + 21.600x
d) y = 21.600 + 14.354x

Use the regression line equation to predict the temperature when the chirp rate is 3.2 chirps/second. Round to one decimal place.
_____ºF

Answer 1

Y - My X - My -0.800 0.600 0.500 -1.200 0.200 0.700 -5.633 16.067 4.267 -20.533 -2.433 8.267 (X - My)2 0.640 0.360 0.250 1.440 0.040 0.490 (Y - My)? 31.734 258.138 18.204 421.618 5.921 68.338 (X - Mx)(Y - My) 4.507 9.640 2.133 24.640 -0.487 5.787 Mx: 3.200 My: 67.533 Sum: 3.220 Sum: 803.953 Sum: 46.220

Correlation coefficient r = E Coc - Moc) (ya My) * Calculated datter are as above. Vere - Alok) €(-Hy) 46. 563.22) (803.953) 46.22 50,899 . o.gos r = 0.908 у => Regresion Line bixta Here b=(x-Moc) (y-My) (x-Mac)? 26.22 3.22 = 14. 354 ý -boo V = Eying Egis 405. 2 -67.533 - 67.533- 14.35463.28) |Fixie 1972 J 3. २२ - 21. 313 = 21. GOO

→ The correct Ans Co y = 21.600 + 14.35400 > Now Predict temperature when chirp Rate is 3.2 Putting the value in equation Y = 21.600 +14.354 (3.3) 67.5 - 67.5°F