Question

Use the following set of data to answer the question: is there a significant association between an immigrant’s length of time in the country and his/her level of acculturative stress, as measured by a well-being scale? The data are listed in the table below. Years Well-being In country score X Y 12 6 15 8 9 4 7 5 18 9 24 10 15 7 16 6 21 3 15 9 M = 15.20 M = 6.70 SSx = 235.60 SSy = 48.10 a. Calculate SP = , and then calculate r = . (5 points) b. Give the critical value = , and determine the significance of this correlation at alpha .05, two-tailed. (3 pts.) c, Find the regression equation for predicting the level of acculturative stress an immigrant would experience if s/he had been in the country 30 years (5 pts)

Answer 1

X	Y	XY	X²	Y²
12	6	72	144	36
15	8	120	225	64
9	4	36	81	16
7	5	35	49	25
18	9	162	324	81
24	10	240	576	100
15	7	105	225	49
16	6	96	256	36
21	3	63	441	9
15	9	135	225	81
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
152	67	1064	2546	497

Sample size, n =    10

x̅ = Ʃx/n = 152/10 =    15.2

y̅ = Ʃy/n = 67/10 =    6.7   

SSxx = Ʃx² - (Ʃx)²/n = 2546 - (152)²/10 =    235.6

SSyy = Ʃy² - (Ʃy)²/n = 497 - (67)²/10 =    48.1

SP = Ʃxy - (Ʃx)(Ʃy)/n = 1064 - (152)(67)/10 =    45.6

--

Correlation coefficient, r = SP/√(SSxx*SSyy) = 45.6/√(235.6*48.1) = 0.4284

--

Critical value, rc = 0.632

--

As |r| < rc, we fail to reject the null hypothesis. there is no correlation between x and y.

--

Slope, b = SSxy/SSxx = 45.6/235.6 =    0.193548387

y-intercept, a = y̅ -b* x̅ = 6.7 - (0.19355)*15.2 =    3.758064516

Regression equation :   

ŷ = 3.7581 + (0.1935) x  

Predicted value of y at x =    30

ŷ = 3.7581 + (0.1935) * 30 = 9.5645