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. 1. Find the correlation coefficient for the data. Round to three decimal places. 2. Find the least-squares regression line equation for predicting the temperature, y, from the chirp rate, X. Choose the correct answer. Oy = -0.683 + 0.057x Oy = 0.057 -0.683x Oy = 14.354 + 21.600x Oy = 21.600 + 14.354x 3. Use the regression line equation to predict the temperature when the chirp rate is 3.2 chirps/second. Round to one decimal place. °F

Answer 1

fx С D E F LJI 2380 2381 obs. no. 1 2382 Chirp rate (x) temperature (y) 2.4 61.9 3.8 83.6 3.7 71.8 2383 2 2384 3 2385 4 2 47 2386 3.4 5 6 Total 65.1 75.8 2387 3.9 2388 19.2 405.2 2389 2390 2391 2392 2393 3.2 X bar Y bar 2394 67.53333333 2395 2396 r 2397 sigma_y sigma_x 0.908419787 11.57550095 0.732575366 2398 2399 2400 byx 14.35403727 2401 2402 2403 2404 2405 2406 2407 2408 + Sheet1 Sheet2

O Correlation Coefficient 0.908 CORREL (arrays, away 2) CORREL (x, y) - = 0.908 - {Using MS-Excel} 27 Y = 21.600 + 14.3548 Since, Regression eqr. Y on x is, y-T = byse (x-) : y = ý + byge*x - bygex where » Y= Ý - bya ă + bye x Ý - AVERAGE () = 67.53 AVERAGE STDEV.P (4) 11.5755 STDEVIP (*) 0.73267 3.2 67 68 byx =8. oy - or Oo9084x 01.5755 6-19 0.73257 140354 - Y= 67.53 - (14.354 * 312) +14.354 X 21.600 + 14.3548 = when is 3.2 = The temperature Chirp rate 6751 F y = = 21.600 +14.354 X 21.600 + (14,354 * 3.2) = = 67.5 }