Suppose a researcher gathered survey data from 19 employees and asked the employ

Question

Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the following data represent the results of this survey. Assume that relationship with their supervisor is rated on a scale from 0 to 50 (0 represents a poor relationship and 50 represents an excellent relationship); overall quality of the work environment is rated on a scale from 0 to 100 (0 represents poor work environment and 100 represents an excellent work environment); and opportunities for advancement is rated on a scale from 0 to 100 (0 represents no opportunities and 100 represents excellent opportunities). Answer the following questions: a) What is the regression formula based on the results from your regression? b) How reliable do you think the estimates will be based on this formula? Explain your answer by citing the relevant metrics. c) Are there any variables that do not appear to be good predictors of job satisfaction? How can you tell? d) If a new employee reports that her relationship with her supervisor is 40, rates her opportunities for advancement to be at 30, finds the quality of the work environment to be at 75, and works 60 hours per week, what would you expect her job satisfaction score to be? Job satisfaction Relationship with supervisor Opportunities for advancement Overall quality of work environment Total hours worked per week 55 27 42 50 52 20 35 28 60 60 85 40 7 45 42 65 35 48 65 53 45 29 32 40 58 70 42 41 50 48 35 22 18 75 55 60 34 32 40 50 95 40 48 45 40 65 33 11 60 38 85 38 33 55 47 10 5 21 50 62 75 37 42 45 43 80 37 46 40 42 50 31 48 60 46 90 42 30 55 38 75 36 39 70 43 45 20 22 40 42 65 32 12 55 53 2a: formula ? 2b: reliability? 2c: variables? 2d: expected score?

Explanation / Answer

We use Excel to solve this problem. We copy the data to Excel in order to analyse it.

Here, y = job satisfaction and the independent variables (x's) are relationship with supervisor, opportunities for advancement, overall quality of work environment and total hours worked per week.

(a) We first fit a linear regression line to the data. We use the Data Analysis option in Excel to do this. The regression equation comes out to be:
job satisfaction = 98.33 + (1.32*relationship with supervisor) + (0.08*opportunities for advancement) - (0.17*overall quality of work environment) - (1.52*total hours worked per week).

(b) The estimates from the regression model will be reliable because the F test for overall significance of the model has yielded a p-value less than 0.05 level of significance. This helps us to conclude that at least one of the independent variables affect the dependent variable. The R-squared value is 0.82 which means that 82% of the variation in the dependent variable is explained by this linear regression model. This high R squared value and the F test establishes the reliability of the model.

(c) In the regression output, we observe that 2 variables - opportunities for advancement and overall quality of work environment have p-values greater than 0.05 level of significance. They are not statistically significant and do not appear to be good predictors.

(d) Putting the values in the regression model stated above, the estimated job satisfaction score is = 49.48 = 49 (approx.)

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