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A regional retailer would like to determine if the variation in average monthly store sales​ can,...

A regional retailer would like to determine if the variation in average monthly store sales​ can, in​ part, be explained by the size of the store measured in square feet. A random sample of

21 stores was selected and the store size and average monthly sales were computed. The results are shown in the accompanying table. Complete parts a through c below. Use a

.005 significance level where needed.

Store Size (Sq. Feet),Average Monthly Sales ($)
17520,577137.00
16040,524885.00
17170,613951.00
17240,561460.00
15960,548223.00
20050,680958.00
15440,537733.00
17170,573223.00
12370,464647.00
12880,510700.00
15530,603630.00
13040,511232.00
21570,722267.00
14580,496209.00
16560,609329.00
14990,550325.00
18720,616300.00
18840,612865.00
16300,667022.00
20080,713078.00
18380,547447.00

Calculate the sample correlation coefficient between store size and average monthly sales.

The correlation coefficient is ___.

math   Statistics-And-Probability   
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Answer #1
X Y XY X² Y²
17520 577137 10111440240 306950400 333087116769
16040 524885 8419155400 257281600 275504263225
17170 613951 10541538670 294808900 376935830401
17240 561460 9679570400 297217600 315237331600
15960 548223 8749639080 254721600 300548457729
20050 680958 13653207900 402002500 463703797764
15440 537733 8302597520 238393600 289156779289
17170 573223 9842238910 294808900 328584607729
12370 464647 5747683390 153016900 215896834609
12880 510700 6577816000 165894400 260814490000
15530 603630 9374373900 241180900 364369176900
13040 511232 6666465280 170041600 261358157824
21570 722267 15579299190 465264900 521669619289
14580 496209 7234727220 212576400 246223371681
16560 609329 10090488240 274233600 371281830241
14990 550325 8249371750 224700100 302857605625
18720 616300 11537136000 350438400 379825690000
18840 612865 11546376600 354945600 375603508225
16300 667022 10872458600 265690000 444918348484
20080 713078 14318606240 403206400 508480234084
18380 547447 10062075860 337824400 299698217809
Ʃx = Ʃy = Ʃxy = Ʃx² = Ʃy² =
350430 12242621 207156266390 5965198700 7235755269277

Sample size, n = 21

SSxx = Ʃx² - (Ʃx)²/n = 5965198700 - (350430)²/21 = 117523228.6

SSyy = Ʃy² - (Ʃy)²/n = 7235755269277 - (12242621)²/21 = 98528176437

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 207156266390 - (350430)(12242621)/21 = 2861900817

Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 2861900817.14285/√(117523228.57143*98528176436.9521) = 0.8410

Null and alternative hypothesis:

Ho: ρ = 0 ; Ha: ρ ≠ 0

Test statistic :  

t = r*√(n-2)/√(1-r²) = 0.841 *√(21 - 2)/√(1 - 0.841²) = 6.7765

df = n-2 = 19

p-value = T.DIST.2T(ABS(6.7765), 19) = 0.0000

Conclusion:

p-value < α Reject the null hypothesis. There is a correlation between x and y.

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