a) State the population regression with appropriate variable names b) Assess the
ID: 3319996 • Letter: A
Question
a) State the population regression with appropriate variable names
b) Assess the overall fit of the model using both the adjusted R^2 and an F test. Clearly explain.
c) Conduct a test of each independent variable at alpha= .05. Which variables are statistically significant?
d) Does it make a difference if an employee has a technical or clerical job? Explain.
e) Does gender matter? If so, by how much? Explain.
f) Predict the average monthly salary for a 23 years old female worker with 70 months of service in a technical job. Round to two decimals.
g) Find the 95% confidence interval for the monthly salary described in part f.
As part of your yearly report to the Mark Zuckerberg, you are required to present an analysis of the salaried Name: employees. Because there are over 17,000 employees, you do not have the staff to gather information on each salaried employee, so you select a random sample of 30. For each employee, you record monthly salary, service at FB, in months; age; gender (1 - male, 0 - female); and whether the employee has a technical or clerical job. Those working technical jobs are coded 1, and those who are clerical 0 Monthly Length of Monthly Length of Sal 3729 4186 3858 3819 3350 Gender Gender Sal 3769 3740 3941 4367 4467 3640 3756 3706 3767 3200 3706 3985 3555 3749 4056 Service Service 93 104 104 126 98 42 129 97 101 0 46 39 43 35 40 59 30 60 45 32 42 57 100 4030 4550 3544 3766 3937 3691 3623 123 94 96 124 73 110 90 104 35 46 56 23 67 36 53 107 105 86 3791 56 4001 95 30 106 45 3874Explanation / Answer
The overall coefficient of linear regression is :
a. Y = 2651.8575 + 13.4219*Length of Service - 6.7102*Age + 205.6455*Gender - 33.4530*Job
b. Adj Rsquare = .3419 and the F-test reveals a Fvalue of 4.7672 with a p-value of .0054 which is less than .05, indicating significant
fit of data to the model. The model is significant
R square of .3419 reveals that the 34.19% variance in dependent variable is being explained by the independent variable
c.Variables with p-value less than .05 are statistically significant. Hence, Length of Service, Gender are statistically significant.
d. It doesn't matter. because the variable is statistically insignificant. We know this from the more than .05 p-value the variable "Job" has got. It has a p-value of .7119 indicating that the variable is not-significant
e. Yes, it does. A male earns $205.6455 more than a female. The p-value is .0315 which is much less than .05, indicating that Gender is statistically significant and therefore matters
f. This should be :
Y = 2651.8575 + 13.4219*(70 for months of service)- 6.7102*(23 is age) + 205.6455*(0 for female) - 33.4530*(0 for technical)
= $3437.06
g. The 95% CI is given by : Y^ + Z*SE = 3437.06 +/- 1.96*236.5292 = $2973.46 to $3900.66
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.