# Statistics of simple regression analyses

Using Excel as your processing tool, work through three simple regression analyses.

First run a regression analysis using the BENEFITS column of all data points in the AIU data set as the independent variable and the INTRINSIC job satisfaction column of all data points in the AIU data set as the dependent variable. Create a graph with the trendline displayed. What is the least squares regression line equation? What are the slope and the y-intercept? What is the R-squared value?

Next, run a regression analysis using the BENEFITS column of all data points in the AIU data set as the independent variable and the EXTRINSIC job satisfaction column of all data points in the AIU data set as the dependent variable. Create a graph with the trendline displayed. What is the least squares regression line equation? What are the slope and the y-intercept? What is the R-squared value?

Next, run a regression analysis using the BENEFITS column of all data points in the AIU data set as the independent variable and the OVERALL job satisfaction column of all data points in the AIU data set as the dependent variable. Create a graph with the trendline displayed. What is the least squares regression line equation? What are the slope and the y-intercept? What is the R-squared value?

Finally, make very specific comments and give reasons regarding any similarities or differences in the output results. Which regression produces the strongest correlation coefficient result? Why?

Be sure to provide references in APA format for any resources you may use.

Instructor Comments:

In the first three parts you will do three regression lines, that are INTRINSIC = b * BENEFITS + a, EXTRINSIC = b * BENEFITS + a, and OVERALL = b * BENEFITS + a. Page 546 has directions on how to compute correlations and regression lines in Excel. Use all 25 data rows of the three columns, no samples no extra numbers, and no partitioning!

Be sure to present three regression equations with R-squared value and three graphs. Provide the following summary table.

Make an XY (scatter) plot and include the trendline. In Excel, you need to highlight the two columns you want to graph to make the scatter gram. In Office 2007 which is the official AIU version, under insert is all of the graphs. You need to have the graph highlighted then under layout is trendline. In Office 2003, after you have made the scatter plot, there is an "add trendline" option under the Chart menu. Don't forget to do the fourth part. Write this as a coherent integrated report with an introduction, description of methods, results, interpretation of results, and conclusion, with references.

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#### Solution Preview

Job satisfaction survey

Following Regression output is obtained using Excel Data Analysis tool for the variables "Benefits" and "Intrinsic job satisfaction".

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.043499

R Square 0.001892

Adjusted R Square -0.0415

Standard Error 0.853805

Observations 25

ANOVA

df SS MS F Significance F

Regression 1 0.031786 0.031786 0.043603 0.836433

Residual 23 16.76661 0.728983

Total 24 16.7984

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 5.616646 1.013686 5.540816 1.23E-05 3.51968 7.713612

BENEFITS -0.04143 0.198411 -0.20881 0.836433 -0.45188 0.369014

From the above Regression output, we have the following analyzed information.

The least Squares Regression line equation using "Benefits" as independent variable and "Intrinsic job satisfaction" as the dependent variable is as follows:

INTRINSIC JOB SATISFACTION = - 0.0414*BENEFITS + 5.6166

Where the slope = - 0.0414 and y-intercept = 5.6166

The R-squared value reported in the above regression is = 0.001892

Following is the scattergraph with trendline for the variables "Benefits" as independent variable and "Intrinsic job ...

#### Solution Summary

The solution examines the statistics of simple regression analyses.