Question 5 The manager of Colonial Furniture has been reviewing w 6 months, all

Question

Question 5 The manager of Colonial Furniture has been reviewing w 6 months, all advertisem per week has varied from one to seven. The sto customers who enter the store each week. The number of ads and the n for the past 26 weeks were recorded. The manager b higher the number of customers that arrive at his store a. Create a suitable table in Excel that will help you calculate a and b for an estimated regression of the form Y =a+bX b. C eekly advertising expenditures. During the past ents for the store have appeared in the local newspaper. The number of ads re's sales staff has been tracking the number of umber of customers per week elieves that the higher the number of ad s the reate another table in Excel that will help you calculate the residuals and, subsequently, the R- squared value for the model. Based on the R-squared value, does the estimated regression provide a good fit of the data?

Explanation / Answer

Ans:

a)

Regression Equation(y) = a + bx

Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)

Intercept(a) = (Y - b(X)) / N

slope,b=(26*43025-107*10005)/(26*527-107^2)=21.356

y-intercept,a=(10005-21.356*107)/26=296.92

Regression eqn:

y'=296.92+21.356x

b)

R2=1-(SSE/SSTO)

SSE=424281.17

SSTO=463802.04

R2=1-(424281.17/463802.04)=0.0852

As,R2=0.0852,which indicates that only 8.52% of the linear variation in dependent variable is due indpendent variable,which is very less,so it does not represent a good fit of data.

ads(x) customer(y) xy x^2 y^2 y'=21.356x+296.92 (y-y')^2 (y-mean(y))^2 1 5 353 1765 25 124609 403.70 2570.49 1011.88 2 6 319 1914 36 101761 425.06 11247.88 4330.96 3 3 440 1320 9 193600 360.99 6242.90 3045.94 4 2 332 664 4 110224 339.63 58.25 2788.90 5 4 172 688 16 29584 382.34 44244.60 45288.10 6 2 331 662 4 109561 339.63 74.51 2895.52 7 4 344 1376 16 118336 382.34 1470.26 1665.46 8 2 483 966 4 233289 339.63 20554.38 9641.28 9 4 329 1316 16 108241 382.34 2845.58 3114.76 10 2 532 1064 4 283024 339.63 37005.45 21664.90 11 7 496 3472 49 246016 446.41 2458.97 12363.22 12 5 393 1965 25 154449 403.70 114.49 67.08 13 4 376 1504 16 141376 382.34 40.25 77.62 14 7 372 2604 49 138384 446.41 5537.15 164.10 15 2 512 1024 4 262144 339.63 29710.73 16177.30 16 5 254 1270 25 64516 403.70 22410.09 17111.26 17 5 459 2295 25 210681 403.70 3058.09 5504.16 18 2 153 306 4 23409 339.63 34831.50 53735.88 19 1 426 426 1 181476 318.28 11604.46 1696.62 20 6 566 3396 36 320356 425.06 19865.21 32829.82 21 6 596 3576 36 355216 425.06 29221.85 44601.22 22 5 395 1975 25 156025 403.70 75.69 103.84 23 6 676 4056 36 456976 425.06 62972.89 84791.62 24 3 194 582 9 37636 360.99 27884.99 36408.46 25 2 135 270 4 18225 339.63 41874.26 62405.04 26 7 367 2569 49 134689 446.41 6306.27 317.20 Total= 107 10005 43025 527 4313803 424281.17 463802.04 mean(y)= 384.81 (SSE) (SSTO) Slope,b= 21.356 R^2= 0.0852 y,intercept,a 296.920

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