Sorry I was a bit disorganized in today's lesson....the gnome costume threw me off....
This weekend, please complete the following questions regarding linear regression (lines of best fit). These were given to you on a handout in class; if you lost it, the questions are below:
The following table gives the time spent on a job (in years) and the amount of money earned (in dollars):
Time
|
0
|
1
|
5
|
10
|
Earnings
|
20,000
|
22,000
|
30,000
|
40,000
|
a. Write an equation for the linear regression.
b. What is the value of the correlation, r? Interpret its meaning (comment on the
strength and direction of the correlation).
c. Use your equation from (b) to find the earnings
for an employee who has spent 7 years at this company.
d. Find the earnings for an employee who has worked
for 6 months.
e. How long would we estimate an employee has
worked at the company if he/she earns $34,000?
f . How long would you expect an employee to work
before they earn $100,000?
Here are some tips for using your calculator (for questions a and b):
- Use this link to create a scatter plot: http://calculator.maconstate.edu/scatterplot/index.html
- Use this link to find the regression equation: http://calculator.maconstate.edu/linear_regression/index.html
- **If your calculator does not give you r and R^2, you first need to set it to do so. Press 2nd, zero to go to the catalog. Then, scroll down and select "DiagnosticOn." Press enter twice. This sets our calculator to show r; now, do the steps to find the regression equation again (LinReg) and it'll show these values.
Finally, here are the answers to your homework, so you can make sure you're doing everything correctly:
a. y = 2,000x + 20,000
b. r = 1; this is a perfect (strongest possible), positive correlation. As time spend on a job increases, so does the amount of money earned.
c. y = 2,000(7) + 20,000 = $34,000
d. y = 2,000(0.5) + 20,000 = $21,000
e. 34,000 = 2,000x + 20,000; x = 7 years
f. 100,000 = 2,000x + 20,000; x = 40 years
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