Question

from part 5-12 plz dont do 1-4

BUNUS Assignment! A Sample Data AnalySIS III Licer Please answer all of the following questions. Make sure you show all your work, providing snapshots from Excel as well as listing all formulas and relevant explanation, as needed. We are interested in exploring the relationship between the income of professors (measured in thousands of dollars) and the number of years they have been employed by the university. We collect the following data from eight professors. Years of Employment Income 14 69. 7 23 71.2 1419 68.2 71.5 19 69.7 12 70.1 104 67.6 66.1 1. Calculate the covariance between the two variables in Excel. Provide a snapshot of your work in Excel, and explain each step with reference to the formula studied in class. (Let x = Years and y = Income.) 2. Calculate the sample correlation coefficient. Once again, show your work in Excel. 3. Plot a scatter diagram in Excel, measuring years of employment on the x-axis, and income level on the y-axis. What does a scatter diagram tell you about the relationship between x and y using the given data points? 4. Run the simple linear regression analysis of income on length of employment. 5. What is the estimated regression line? 6. What is the estimated income for a professor with 20 years of employment? 7. How would you interpret the slope coefficient bı? 8. Is it possible to provide a meaningful interpretation of the intercept of the sample regression line? 9. Compute the coefficient of determination. Show that your answer is the same as that reported in the Excel output. How would you interpret the coefficient of determination? 10. Compute the regression sum of squares, SSR, and the error sum of squares, SSE. 11. Test the null hypothesis that the population slope is zero using the t-test: HO: B1 = 0 vs. H1: B10 12. Test the hypotheses Ho: B1 = 0 vs. H :B10 using the statistic.

Answer 1

The regression results in Excel are as below: SUMMARY OUTPUT Regression Statistics Multiple R 0.87528625 R Square 0.76612602 Adjusted R Square 0.727147024 Standard Error 0.961931732 Observations ANOVA df F Significance F 19.654842 0.004407073 Regression Residual Total 1 6 SS M S 18.18687406 18.18687 5.551875938 0.925313 23.73875 Coefficients Intercept 65.38434217 Years of employmen 0.269784892 Standard Error Stat P-value Lower 95% 0.938549642 69.6653 5.88567E-10 63.08779393 0.06085312 4.433378 0.004407073 0.120882673 Estimated regression line: Income = 65.38 +0.269 Years of employment When years of employment = 20, then income will be: Income = 65.38 +0.269 Years of employment Income = 65.38 +0.269 (20) Income = $70.76 thousand

7. Slope coefficient = 0.269 Interpretation: An increase in the years of employment by 1 year leads to an increase in income by 0.269 thousand dollars 8 Yes It means when the years of employment are 0, or when the individual is a fresher in the job market, his base wage would be close to $65.38 thousand

Note: First 4 subparts of asked questions (5-12) are answered as below.