Question

Complete all of the parts of these questions using SPSS to carry out computations and to produce the scatterplot. Turn in the SPSS printouts with your assignment.

1.    Using the data set below:

1. Compute the Pearson product-moment correlation coefficient between X and Y. Describe the nature of the relationship between X and Y.
2. Compute the coefficient of determination for this correlation. What additional information does the coefficient of determination give you about the relationship between X and Y?
3. Obtain the linear regression equation for predicting Y based on X.
4. Construct a scatterplot of the data for the X and Y variables. How does the scatterplot help you to describe the relationship between X and Y?

Participant	X	Y	Participant	X	Y	Participant	X	Y
1	72	150	11	80	235	21	75	165
2	70	125	12	63	180	22	66	130
3	77	220	13	74	185	23	60	110
4	58	150	14	61	125	24	64	115
5	65	155	15	69	230	25	63	145
6	68	195	16	78	200	26	72	200
7	70	140	17	57	105	27	70	190
8	85	250	18	61	135	28	89	240
9	71	140	19	60	175	29	66	200
10	69	175	20	70	145	30	71	175

2. Use SPSS to calculate a, b, and c for the data on Divorce Rate and Unemployment in Practice Problem #1.

1.    Calculate the Pearson product-moment correlation coefficient between X and Y.
2.    Calculate the slope and intercept for the linear regression equation for predicting Y

                     based on X.

3.    Construct a scatterplot of the data for the X and Y variables.
4.    Compare these results with those you got by han Are there differences? Discuss why, or why not.

Answer 1

a)

Correlations
		X	Y
X	Pearson Correlation	1	.732**
	Sig. (2-tailed)		.000
	N	30	30
Y	Pearson Correlation	.732**	1
	Sig. (2-tailed)	.000
	N	30	30

The Pearson product-moment correlation coefficient between X and Y is 0.732 and more than 0.50. Hence, we can conclude that the variable X and Y has a strong positive association.

b) The coefficient of determination for this correlation is equal to the square of the Pearson product-moment correlation coefficient. Therefore, the coefficient of determination=0.732^2=0.5358. Hence, 53.58% variation of the response variable Y can be explained by the variable X.

c)

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	-98.049	47.407		-2.068	.048
	X	3.870	.682	.732	5.677	.000

The linear regression equation for predicting Y based on X is

Y^= -98.049 +3.870 *X.

d)

From the scatter plot of variables X and Y, we can conclude that increase the value of X increases the value of Y and vice-versa. It has the same meaning as the above correlation coefficient.