# Correlation and Regression calculations

**Question description**

Week 5 Correlation and Regression For each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. 1 Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.) a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work? 2 Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid, age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways of expressing an employee’s salary, we do not want to have both used in the same regression.) Ho: The regression equation is not significant. Ha: The regression equation is significant. Ho: The regression coefficient for each variable is not significant Ha: The regression coefficient for each variable is significant Sal The analysis used Sal as the y (dependent variable) and SUMMARY OUTPUT mid, age, ees, sr, g, raise, and deg as the dependent variables (entered as a range). Regression Statistics Multiple R 0.992154976 R Square 0.984371497 Adjusted R Square 0.981766746 Standard Error 2.592776307 Observations 50 ANOVA df SS MS F Significance F Regression 7 17783.65546 2540.522209 377.9139269 8.44043E-36 Residual 42 282.3445372 6.72248898 Total 49 18066 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -4.009 3.775 -1.062 0.294 -11.627 3.609 -11.627 3.609 Mid 1.220 0.030 40.674 0.000 1.159 1.280 1.159 1.280 Age 0.029 0.067 0.439 0.663 -0.105 0.164 -0.105 0.164 EES -0.096 0.047 -2.020 0.050 -0.191 0.000 -0.191 0.000 SR -0.074 0.084 -0.876 0.386 -0.244 0.096 -0.244 0.096 G 2.552 0.847 3.012 0.004 0.842 4.261 0.842 4.261 Raise 0.834 0.643 1.299 0.201 -0.462 2.131 -0.462 2.131 Deg 1.002 0.744 1.347 0.185 -0.500 2.504 -0.500 2.504 Interpretation: Do you reject or not reject the regression null hypothesis? Do you reject or not reject the null hypothesis for each variable? What is the regression equation, using only significant variables if any exist? What does result tell us about equal pay for equal work for males and females? 3 Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions. Note: be sure to include the appropriate hypothesis statements. 4 Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not? Which is the best variable to use in analyzing pay practices - salary or compa? Why? 5 Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question? What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?

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