Mop and Broom Manufacturing has tracked the number of units sold of their most p

Question

Mop and Broom Manufacturing has tracked the number of units sold of their most popular mop over the past twenty-four months. This is shown. Month Sales Month Sales Month Sales 1 234 9 319 17 362 2 246 10 340 18 379 3 261 11 348 19 363 4 257 12 358 20 380 5 268 13 352 21 396 6 285 14 359 22 393 7 385 15 379 23 407 8 304 16 354 24 411 Develop a linear trend line for the data. (Round your answer to 2 decimal places, the tolerance is +/-0.01.) Sales = + (month) Compute a correlation coefficient for the data and evaluate the strength of the linear relationship. (Round your answer to 2 decimal places, the tolerance is +/-0.01.) Correlation coefficient is . It indicates linear relationship. (Use not rounded amounts to answer this question.) Using the linear trend line equation, develop a forecast for the next period,month 25. (Round your answer to 2 decimal places, the tolerance is +/-0.01. Do not round intermediate results used to achieve this answer.) Forecast for month 25 =

Explanation / Answer

MONTH, x SALES, y x*y x^2 y^2 1 243 243 1 59049 (a) 2 247 494 4 61009 n 24 3 259 777 9 67081 4 255 1020 16 65025 Slope 5 272 1360 25 73984 a=n*sum(x*y) 2635992 6 274 1644 36 75076 b=sum(x) * sum(y) 2443200 7 389 2723 49 151321 c=n*sum(x^2) 117600 8 295 2360 64 87025 d = sum (x) ^2 90000 9 319 2871 81 101761 10 335 3350 100 112225 slope, m = (a - b) / (c - d) 11 338 3718 121 114244 m 6.99 12 344 4128 144 118336 13 358 4654 169 128164 Y intercept 14 372 5208 196 138384 e= sum(y) 8144 15 385 5775 225 148225 f = m* sum(x) 2095.57 16 349 5584 256 121801 y-intercept, b = (e - f) / n 17 378 6426 289 142884 y -intercept 252.02 18 387 6966 324 149769 19 372 7068 361 138384 Trend line: 20 381 7620 400 145161 Sales = 252.02 + 6.99 (month) 21 395 8295 441 156025 22 389 8558 484 151321 23 401 9223 529 160801 24 407 9768 576 165649 Sum 300 8144 109833 4900 2832704 (b) avg x 12.5 avg y 339.3333 Formula for correlation coefficient , r : r = [n* sum (xy) - sum(x)*sum(y)]/[sqrt{(n*sum(x^2)-sum(x)^2}{n*sum(y^2)-sum(y)^2}] r 0.9007 positive r means, a positive relationship between x and y Since the value of r is close to +1, it implies a strong positive correlation between Month and Sales c) Forecast for the month 25 = 427 ( = 252.02 + 6.99 * 25 ) (value is rounded off)

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