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

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Basic Math

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, x24327541761073246112
Sales, y765819011214123524147188

(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)

a)

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

b)

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

c)

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