Practice Exam question PLEASE HELP 26. A lawn and garden centre intends to use s
ID: 467058 • Letter: P
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Practice Exam question PLEASE HELP
26. A lawn and garden centre intends to use sales of lawn fertilizer to predict lawn mower sales. The store manager wishes to determine the relationship between fertilizer and mower sales. The pertinent data are: LO6 Number Number Fertilizer of Fertilizer of Sales Mowers Sales Mowers Period (tonnes) Sold Period (ton Sold 1.6 10 8 13 1.3 1.7 1.8 11 10 12 4 2.0 11 19 2.2 1.4 13 17 1.5 a. Determine the correlation between the two vari- ables. Does it appear that arelationship between these variables will yield good predictions? Explain. (You may use Excels CORREL (RangeY,RangeX) to determine r, where RangeY is the range of Excel cells containing they values and Range) is the range of Excel cells containing the x values. You also need R2, RSQ(RangeY, RangeXO. b. obtain a linear regression line for the data. You may use Excel's slopeRangeY, RangeXy and interce to obtain the regression coefficients b and a, respectively. Alterna tively, use Trendline in the Layout menu) c. Predict lawn mower sales, given fertilizer sales of 2 tonnes.Explanation / Answer
Period X (fertilizer sales) Y ( lawn mowers sales) XY X*X 1 1.6 10 16 2.56 2 1.3 8 10.4 1.69 3 1.8 11 19.8 3.24 X= 21.2 4 2 12 24 4 Y = 122 5 2.2 12 26.4 4.84 XY = 205.4 6 1.6 9 14.4 2.56 X*X = 35.62 7 1.5 8 12 2.25 8 1.3 7 9.1 1.69 X-bar = X/ no.of observations = 21.2/13 = 1.630769 9 1.7 10 17 2.89 10 1.2 6 7.2 1.44 Y-bar = Y/no.of observations = 122/13 = 9.384615 11 1.9 11 20.9 3.61 12 1.4 8 11.2 1.96 n= no.of observations 13 1.7 10 17 2.89 21.2 122 205.4 35.62 Answer A and B To find correlation between fertilizer sales ( X) and Mowers sold ( Y) , formula is Y = a+bX b=( XY - n(X-bar) (Y-bar))/ ( X*X-n ( X-bar)*(X-bar)) and a = Y-bar - b * X-bar b = (205.4 - 13 ( 1.63)(9.38))/ 35.62 - 13 (1.63)(1.63) b = 205.4 - 198.76 / 35.62 - 34.54 a= 9.38 - 6.148*1.63 a = 9.38 - 10.02 b= 6.64 / 1.08 a = -0.64121 b= 6.148 thus Y = -0.64121 + 6.148 * X Sin ce , there is strong linear relation between two variable X and Y, X is a good predictor of Y. Answer C Predicted lawn mowers sale ( Y ) = -0.64121 + 6.148 * 2 ( Here X = fertilizer sales = 2 tonnes) Y = -0.64121 + 12.296 Y= 11.654 Hence expected no.of lawn mowers sale = 12 if , fertilizer sales is 2 tonnes.
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