Simple Linear Regression

Simple Linear Regression

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Depression Scores	Income in Thousands	Job Satisfaction
22	45	5
56	75	10
43	23	3
78	64	8
22	41	4
96	84	10
44	55	5
27	36	7
71	65	8
88	48	9

Compute a correlation/regression analysis using this set of numbers and write up the results in APA format. Note that higher scores are indicative of greater levels of depression.

	Regression Statistics
	Multiple R			0.856644
	R Square			0.733839
	Adjusted R Square			0.657793
	Standard Error			1.470887
	Observations			10
	ANOVA
				df		SS		MS		F
	Regression			2		41.75544		20.87772		9.649938
	Residual			7		15.14456		2.163508
	Total			9		56.9
		Coefficients	Standard Error		t Stat		P-value		Lower 95%		Upper 95%
Intercept		0.982813	1.484688		0.661966		0.529175		-2.52792		4.493543
Depression Scores		0.035177	0.023815		1.477111		0.183165		-0.02114		0.091491
Income in Thousands		0.074496	0.035042		2.125878		0.071102		-0.00837		0.157358

 

	Depression Scores	Income in Thousands	Job Satisfaction
Depression Scores	1
Income in Thousands	0.661467	1
Job Satisfaction	0.749666	0.80677	1

The linear regression model was conducted to establish the relationship between depression scores, income in thousands, and job satisfaction of employees. The analysis was conducted using an alpha level of .05. The output indicates that the model explains 73% of the relationship between the variables (R-square = 0.733) (Field, 2018). Job satisfaction is taken as the response variable when modeling relationships. The correlation analysis indicates that both income in thousands and depression scores are positively related to job satisfaction. However, the relationship between the variables is not statistically significant since the p-values are greater than .05.

Include confidence intervals in your output and explain what this means.

The confidence levels for the model parameters indicate that the beta values or the intercepts are more likely to fall. For the depression scores, the 95% confidence interval for the intercept is between -0.02114 and 0.091491. For income in thousands, the 95% confidence interval for the intercept is between -0.00837 and 0.157358. The confidence interval for the overall model intercept is between -2.52792 and 4.493543.

References

Field, A. (2018). Introduction to Statistics using IBM SPSS Statistics. London: Cengage Learning.

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Assignment #8
Simple Linear Regression

Depression Scores Income in Thousands Job Satisfaction
22 45 5
56 75 10
43 23 3
78 64 8
22 41 4
96 84 10
44 55 5
27 36 7
71 65 8
88 48 9

1. Compute a correlation/regression analysis using this set of numbers and write up the results in APA format. Note that higher scores are indicative of greater levels of depression.

2. Include confidence intervals in your output and explain what this means.

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