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 supervisor is rated on a scale from 0 to 50 (0 represents 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 evnvirnment), and opportunities for advancement is rated on a scale from 0 to 50 (0represents no opportunities and 50 represents excellent opportunities).
a. what is the regression formula?
b. How reliable do you think the estimates will be based on this formula? How can you tell?
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 relation ship with er supervisor is 40, finds the quality of the work environment to be scored at 75, works 60 hours per week and rates her opportunities for advancement to be at 30, what would you expect her job satisfaction score to be?
example Job satisfaction 55, Relationsjip with supervisor 27, overall quality of work environment 65, total hours worked per week 50 opportunities for advancement 42
To answer the given questions, we need to perform a regression analysis on the provided survey data. Here are the steps to calculate the regression formula and answer the subsequent questions:
Step 1: Organize the data:
Given the survey data, we have information about four variables for each employee - job satisfaction, relationship with supervisor, overall quality of the work environment, and opportunities for advancement. Write down the data in a tabular form to make it easier to analyze.
Employee | Satisfaction | Relationship | Work Environment | Advancement
-------------------------------------------------------------------------
1 | 55 | 27 | 65 | 42
2 | ... | ... | ... | ...
Step 2: Calculate the regression formula:
To find the regression formula, we need to perform a multiple regression analysis, which requires statistical software or tools like Excel, SPSS, or R. These tools will help us estimate the regression coefficients.
The multiple regression formula can be expressed as:
Job Satisfaction = β0 + β1 * Relationship + β2 * Work Environment + β3 * Advancement + ε
In this formula, β0 represents the intercept, β1, β2, and β3 are the regression coefficients associated with Relationship, Work Environment, and Advancement respectively, and ε is the error term.
By running the multiple regression analysis, we can obtain the estimated values of the regression coefficients (β0, β1, β2, and β3), which will form the regression formula.
Step 3: Assess the reliability of the estimates:
To determine the reliability of the estimates, we need to consider several statistics, such as the R-squared value, p-values, and confidence intervals associated with the regression coefficients.
The R-squared value indicates the proportion of variance in the dependent variable (job satisfaction) that can be explained by the independent variables (relationship, work environment, and advancement). A higher R-squared value indicates a better fit of the model.
To assess the significance of each variable's contribution, we can examine the p-values. A smaller p-value suggests that the variable is a significant predictor of job satisfaction.
Additionally, confidence intervals provide a range of values within which we can be reasonably confident that the true regression coefficients lie.
By analyzing these statistics, we can determine how reliable the estimates are and how well the independent variables predict job satisfaction.
Step 4: Identify good predictors of job satisfaction:
To determine if any variables are not good predictors of job satisfaction, we can consider their p-values and assess their significance. Variables with larger p-values indicate weak or insignificant relationships with job satisfaction and may not be good predictors.
By analyzing the individual p-values associated with each independent variable, we can identify the ones that appear to be good or not good predictors of job satisfaction.
Step 5: Use the regression formula to predict job satisfaction:
Once we have the regression formula (from Step 2) and the coefficients, we can use it to predict job satisfaction for a new employee. Using the provided values for the new employee's relationship with supervisor (40), work environment (75), hours worked per week (60), and opportunities for advancement (30), plug those values into the regression formula and calculate the predicted job satisfaction score.
Please note that Steps 2, 3, and 4 involve conducting a statistical analysis, which requires specialized software or tools. You can use software like Excel (with the Data Analysis ToolPak), SPSS, or R to perform these calculations and get accurate results.