You collect data on income (in thousands of dollars) and years of experience of part-time employees working for two companies, and you calculate separate regression equations to explore these linear relationships. The regression equations describing these linear relationships are y1 = 6.7x1 + 2.5 y2 = 7.2x2 + 1.2 Here, y1 and x1 are the expected salary and years of experience for an employee in Company 1, and y2 and x2 are the expected salary and years of experience for an employee in Company 2. Compare expected salaries between an employee at Company 1 with 3 years of experience and an employee at Company 2 with 5.5 years of experience. Which employee has the higher expected salary? A. The employee at Company 1 is expected to make $12,800 more than the other. B. The employee at Company 1 is expected to make $12,800 less than the other. C. The employee at Company 1 is expected to make $18,200 more than the other. D. The employee at Company 1 is expected to make $18,200 less than the other. E. There will be no difference in their expected salaries.
Added by Karen F.
Close
Step 1
We use the regression equation for Company 1, which is \(y_{1}=6.7x_{1}+2.5\). Here, \(x_{1}\) represents the years of experience. Since the employee has 3 years of experience, we substitute \(x_{1}\) with 3. Show more…
Show all steps
Your feedback will help us improve your experience
Lucas Finney and 91 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A researcher wants to determine how employee salaries at a certain company are related to the length of employment, previous experience, and education. The researcher selects eight employees from the company and obtains the following data: Using technology, we have the following multiple regression equation that models the data: Salary, y = 49764 + 364 x1 + 228 x2 + 267 x3, where R^2 = 94.4% You wish to test at alpha=0.05 that whether or not the above model is useful. a) Calculate the test statistic b) Find degrees of freedom c) Find Critical value d) State the statistical decision
Lucas F.
The human resource manager at Gamma, Inc. wants to examine the relationship between annual salaries (Y), the number of years employees have worked at Gamma, Inc. (X1), and whether the employee is male or female (X2). They are also interested in whether the interaction between the two explanatory variables (X1X2) has a significant impact on salaries. These data have been collected for a sample of 28 employees, and the regression output is shown below. Summary measures: Multiple R: 0.8065 R-Square: 0.6504 Adj R-Square: 0.6067 StErr of Estimate: 6572.3 Regression coefficients: Coefficient Std Err t-value p-value Constant 29831.68 3904.56 7.640 0.0000 Years Employed 869.04 266.78 3.258 0.0033 Gender -2396.54 4620.04 -0.519 0.6087 Years & Gender 403.93 350.38 1.153 0.2603 A. Use the information above to estimate the linear regression model. B. Write the regression equation in (A) as two separate equations; one for females and one for males, and interpret the results. C. Would any of the variables in the linear regression model in (A) be considered a dummy variable? Explain your answer. D. Identify and interpret the coefficient of determination (R2) for the model in (A).
Areen D.
A researcher at a large company has collected data on the starting salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their starting salary is y = -2532.7 + 2.12x (x and y are in dollars) and R^2 = 0.49. (a) Predict the current salary of an employee who has a starting salary of $22,000. Show your work clearly. (b) Is the correlation between x and y positive, negative, or zero? How can you tell? Explain briefly. (c) What is the correlation coefficient between the starting salary and current salary? Show your work clearly. (d) What proportion of the variation in current salary is explained by the linear regression model with the starting salary? Show your work clearly.
David N.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD