Question

Use the given data to complete parts​ (a) and​ (b) below.

X              y

2.22.     3.9

4            1.4

3           3.5

4.8          5

​(a) Draw a scatter diagram of the data.

Compute the linear correlation coefficient. The linear correlation coefficient for the four pieces of data is

_______.

​(Round to three decimal places as​ needed.)

​(b) Draw a scatter diagram of the data with the additional data point

left parenthesis 10.4 comma 9.3 right parenthesis(10.4,9.3).

Compute the linear correlation coefficient with the additional data point. The linear correlation coefficient for the five pieces of data is _______

​(Round to three decimal places as​ needed.)

Comment on the effect the additional data point has on the linear correlation coefficient.

A.The additional data point does not affect the linear correlation coefficient.

B.The additional data point weakens the appearance of a linear association between the data points.

C.The additional data point strengthens the appearance of a linear association between the data points.

Explain why correlations should always be reported with scatter diagrams.

A.The scatter diagram is needed to determine if the correlation is positive or negative.

B.The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.

C.The scatter diagram can be used to distinguish between association and causation.

Answer 1

a)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	2.2	3.9	1.6900	0.2025	-0.5850
2	4	1.4	0.2500	4.2025	-1.0250
3	3	3.5	0.2500	0.0025	-0.0250
4	4.8	5	1.6900	2.4025	2.0150
Total	14	13.8	3.8800	6.8100	0.3800
Mean	3.500	3.450	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.074

b)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	2.2	3.9	7.1824	0.5184	1.9296
2	4	1.4	0.7744	10.3684	2.8336
3	3	3.5	3.5344	1.2544	2.1056
4	4.8	5	0.0064	0.1444	-0.0304
5	10.4	9.3	30.4704	21.9024	25.8336
Total	24.4	23.1	41.9680	34.1880	32.6720
Mean	4.880	4.620	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.863

C.The additional data point strengthens the appearance of a linear association between the data points
B.The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.