Use the following information to answer the next four questions. The data in the
ID: 3069396 • Letter: U
Question
Use the following information to answer the next four questions. The data in the table below represent data collected by a university on a salary (in thousands) of 10 randomly selected alumni. The university wanted to determine the pace at which alumni salaries grew over the first 10 years after graduation. The line in the scatterplot is the least squares regression line: y = 29.52 + 7.27x where y is the predicted salary and x is the number of years since graduation.
35. What is the vertical deviation (also known as the residual) for the alumnus in the study who graduated 10 years ago and had the salary of 112 thousand dollars?
9.78
The residual is not positive so it doesn't make sense in this context.
102.22
39.30
2.00
36. Interpret the slope of the regression line in context.
For every 7.27 thousand dollar increase in salary, we expect the years from graduation to increase by one.
For every 29.52 thousand dollar increase in salary, we expect the years from graduation to increase by one.
If the alumnus had just barely graduated (i.e. 0 years), we would expect the average salary to be 29.52 thousand dollars.
For each additional year since graduation, salary increases by 29.52 thousand dollars, on average.
For each additional year since graduation, salary increases by 7.27 thousand dollars, on average.
If the alumnus had barely graduated (i.e. 0 years), we would expect the average salary to be 7.27 thousand dollars.
37. For these data r2 = 0.89, interpret r2 in context.
Salary can be used to predict years since graduation about 89% of the time.
Years since graduation explains 89% of the variation in salary. 89% of the salary is based on years since graduation.
Years since graduation can be used to predict salary about 89% of the time.
38. What is the appropriate conclusion to make about an alumnus who graduated 30 years ago?
The predicted salary is $174.92.
The predicted salary is $145.50.
The predicted salary is $247.62.
We should not use the regression line to make the prediction.
Explanation / Answer
35)
residual =actual -predicted =112-(29.52+7.27*10)=9.78
36)For each additional year since graduation, salary increases by 7.27 thousand dollars, on average.
37)
graduation explains 89% of the variation in salary
38)
We should not use the regression line to make the prediction