Question

Problem Set 1: Linear Regression Analysis

Research Scenario: A community psychologist is interested in whether people’s self-reported degree of religious belief predicts their self-reported feelings of well-being. She administers two questionnaires to 17 individuals, one of which measures degree of religious beliefs (scores range from 1-20 with higher scores indicating higher degree of belief), and another which measures feelings of well-being (scores range from 1-25 with higher scores indicating stronger feelings of well-being). The psychologist compiles the information listed in the table below.

Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether religious belief predicts feelings of well-being. Create a scatterplot with a regression line to show the relationship between the variables.

Degree of Religious Belief	Self-Reported Well-Being
14	19
11	17
19	18
6	10
20	22
18	24
18	17
8	11
12	17
10	9
4	14
19	23
17	21
5	12
15	20
3	8
6	9

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your scatterplot as an APA-style figure as demonstrated in the APA writing presentation. Please write this section in the CORRECT FORMAT. It has to be lengthy and the right equations. Thank you!

Answer 1

Here I attch the SPSS output files also

The two variables Degree of Religious Belief and Self-Reported Well-Being are highly correlated therefore we can fit simple linear regression for the given data.

The correlation between the variables is clear from the scatter plot

From the figure it is clear that the variables are positively correlated and it is confirmed from the correlation table given below.

Pearson correlation coefficient is 0.869.

The fitted linear model is obtained from the model summary

From the table the obtained model is :

From the t test it is clear that the variable is significant since the p value is less than 0.05.From the vif value it is clear that there is no problem of multicollinearity.

The overall adequacy of the model is obtained from the ANOVA table given below

From the p value of F test it is clear that the overall model is significant.since the p value is less than 0.05. Hence we reject the null hypothesis of zero coefficient.

From the QQ plot it is clear that the residuals are normally distrinbuted.

The normality is confimrd using shapiro WIlks test. Tha p value is greater than 0.05 hence we accept the null hpothesis of residuals are normally distrinutrd.

From the R square value is the summary table we can see that 75.4% variation can be explained by the model...