Question

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 ___.

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.