Question

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use

alphaαequals=​0.05.)

x	1010	88	1313	99	1111	1414	66	44	1212	77	55
y	9.149.14	8.148.14	8.738.73	8.788.78	9.269.26	8.118.11	6.136.13	3.093.09	9.149.14	7.267.26	4.734.73

Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot.

Answer 1

(a)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	10	9.14	100	83.5396	91.4
	8	8.14	64	66.2596	65.12
	13	8.73	169	76.2129	113.49
	9	8.78	81	77.0884	79.02
	11	9.26	121	85.7476	101.86
	14	8.11	196	65.7721	113.54
	6	6.13	36	37.5769	36.78
	4	3.09	16	9.5481	12.36
	12	9.14	144	83.5396	109.68
	7	7.26	49	52.7076	50.82
	5	4.73	25	22.3729	23.65
Total	99	82.51	1001	660.3653	797.72

Sample size: n=11

Now,

The coefficient of correlation is :

The critical value of r using table is: 0.553

Since r > 0.553, we can conclude that there is sufficient evidence to support the claim of a linear correlation between the two variables.

(b)

Following is the scatter plot of data:

(c)

Scatter plot shows that relationship between the variables is not linear. It is curvilinear.