Question

# of mirrors                                              locus of control score

                                                      8                                                                     22

                                                      3                                                                     13

                                                      10                                                                  22

                                                      11                                                                  21

                                                      4                                                                     13

                                                      9                                                                     19

                                                      12                                                                  19

                                                      3                                                                     17

                                                      10                                                                  20

                                                      2                                                                     10

                                                      3                                                                     15

                                                      8                                                                     17

                                                      12                                                                  18

                                                      6                                                                     13

                                                      17                                                                  12

                                                      21                                                                  24

                                                      4                                                                     7

                                                      11                                                                  23

                                                      11                                                                  11

                                                      10                                                                  10

Give me the regression equation for the above data.  Also, determine whether there is a significant linear relationship between number of mirrors and locus of control score (be sure to include the null hypothesis tested and decision reached). Use SPSS and 20 participants.

Answer 1

Solution:

Here, we have to use the linear regression model for the prediction of dependent variable locus of control score based on the independent variable number of mirrors. The null and alternative hypotheses for this regression model are given as below:

Null hypothesis: H₀: There is no any statistically significant linear relationship exists between the two variables number of mirrors and locus of control score.

Alternative hypothesis: H_a: There is no any statistically significant linear relationship exists between the two variables number of mirrors and locus of control score.

We assume 0.05 level of significance for this regression model.

The SPSS output for this regression model is given as below:

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.475a	.226	.183	4.49682
a. Predictors: (Constant), Number of Mirrors

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	106.216	1	106.216	5.253	.034a
	Residual	363.984	18	20.221
	Total	470.200	19
a. Predictors: (Constant), Number of Mirrors
b. Dependent Variable: Locus of control score

For this regression model, we get the p-value as 0.034 which is less than the 0.05 alpha level of significance, so we reject the null hypothesis.

There is sufficient evidence to conclude that there is no any statistically significant linear relationship exists between the two variables number of mirrors and locus of control score.

The regression coefficients are given as below:

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	12.085	2.096		5.766	.000
	Number of Mirrors	.482	.210	.475	2.292	.034
a. Dependent Variable: Locus of control score

Regression model is given as below:

Y = 12.085 + 0.482*X