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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Question
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.
Simple Linear Regression
2. Include confidence intervals in your output and explain what this means.
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