Use the data given in the table to answer the following questions. The data represents the average...

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Use the data given inthe table to answer the following questions. The data representsthe average number of miles that a salesperson travels in a dayverses the number of sales made each month.
Miles, x 24 32 75 41 76 107 32 46 112
Sales, y 76 58 190 112 141 235 24 147 188
(a) What is the valueof the correlation coefficient for this set of data? Round to 3decimal places.

(b) What is the equation of the Regression Line for this set ofdata? Round values to two decimal places.

(c) Predict the number of sales an associate could expect to makeif he travelled an average of 108 miles each day. Round to twodecimal places.

Answer & Explanation Solved by verified expert

4.4 Ratings (946 Votes)

x	y	(x-x?)²	(y-y?)²	(x-x?)(y-y?)
24	76	1336.31	2928.01	1978.06
32	58	815.42	5200.01	2059.17
75	190	208.64	3586.68	865.06
41	112	382.42	328.01	354.17
76	141	238.53	118.57	168.17
107	235	2157.09	11001.68	4871.51
32	24	815.42	11259.57	3030.06
46	147	211.86	285.23	-245.83
112	188	2646.53	3351.12	2978.06

	?X	?Y	?(x-x?)²	?(y-y?)²	?(x-x?)(y-y?)
total sum	545	1171	8812.222222	38058.9	16058.44
mean	60.56	130.11	SSxx	SSyy	SSxy

correlation coefficient , r = Sxy/?(Sx.Sy) = 0.877

sample size ,   n =   9
here, x? = ?x / n=   60.56   ,     y? = ?y/n =   130.11

SSxx =    ?(x-x?)² =    8812.2222
SSxy=   ?(x-x?)(y-y?) =   16058.4

estimated slope , ß1 = SSxy/SSxx =   16058.4   /   8812.222   =   1.8223

intercept,   ß0 = y?-ß1* x? =   19.7612

so, regression line is   Y? =   19.76 +   1.82 *x

Predicted Y at X= 108 is
Y? = 19.76119 + 1.822292 * 108 = 216.57

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Miles, x	24	32	75	41	76	107	32	46	112
Sales, y	76	58	190	112	141	235	24	147	188