# Modeling the relationship among annual income, level of education, work experience

#### lalosangeles

##### New member
Hi - I need help with this question. My own attempts are in blue below - it's probably wrong.

Also, I recently downloaded Minitab thinking it will make my life easier, but have no idea how to set up multiple regression so that there's more or less of an automated output.
I know this isn't a Minitab help forum, but if anyone with any knowledge of this can help with this, it'd be much appreciated!

 Work Experience (Years) X₁ Level of Education X₂ Annual Income ($Thousands) Y 12 6 34.7 14 3 17.9 4 8 22.7 16 8 63.1 12 4 33.0 20 4 41.4 25 1 20.7 8 3 14.6 24 12 97.3 28 9 72.1 4 11 49.1 15 4 52.0 We are interested in modeling the relationship among annual income, level of education, and work experience. The level of education is the number of years of education beyond eight grade (1 = completing 1 year of high school, 8 = completing 4 years of college) Use the above data from a random sample of 12 individuals to answer the following. (a) State the regression equation for the scenario. Y' = b X₁ + bX₂ + a Y' = 1.68955X + 5.57296X - 16.31043 (b) Conduct a regression analysis of these data and include your relevant regression output. There must be a way this can simply be done on Minitab... any pointers? (c.) What can you conclude regarding the relationship among annual income, level of education and work experience based on your regression analysis results in part (b)? Cite relevant numeric indices or results of your regression analysis as part of your response. #### tkhunny ##### Moderator Staff member Hi - I need help with this question. My own attempts are in blue below - it's probably wrong. Also, I recently downloaded Minitab thinking it will make my life easier, but have no idea how to set up multiple regression so that there's more or less of an automated output. I know this isn't a Minitab help forum, but if anyone with any knowledge of this can help with this, it'd be much appreciated!  Work Experience (Years)X₁ Level of Education X₂ Annual Income ($ Thousands) Y 12 6 34.7 14 3 17.9 4 8 22.7 16 8 63.1 12 4 33.0 20 4 41.4 25 1 20.7 8 3 14.6 24 12 97.3 28 9 72.1 4 11 49.1 15 4 52.0
We are interested in modeling the relationship among annual income, level of education, and work experience.
The level of education is the number of years of education beyond eight grade (1 = completing 1 year of high school, 8 = completing 4 years of college)
Use the above data from a random sample of 12 individuals to answer the following.

(a) State the regression equation for the scenario.
Y' = b
X₁ + bX₂+ a
Y' =
1.68955X
+ 5.57296X - 16.31043

(b) Conduct a regression analysis of these data and include your relevant regression output.
There must be a way this can simply be done on Minitab... any pointers?

(c.) What can you conclude regarding the relationship among annual income, level of education and work experience based on your regression analysis results in part (b)? Cite relevant numeric indices or results of your regression analysis as part of your response.
Why minitab?
Search "Minitab Multiple Linear Regression". Videos, descriptions, academic papers. There lots of stuff.

The intercept p-value is a little scary. Let's see you demonstrate it.

#### lalosangeles

##### New member
Why minitab?
Search "Minitab Multiple Linear Regression". Videos, descriptions, academic papers. There lots of stuff.

The intercept p-value is a little scary. Let's see you demonstrate it.
This is what I was able to get to... let me know if something looks amiss. Thanks!

a. Annual Income = 1.68955X₁ + 5.57296X₂ - 16.31043

b.

c.
P val of Work Experience < significance level of 0.05.
P val of Level of Education < significance level of 0.05.
Thus, we can conclude that the linear relationship between Work Experience, Level of Education and Annual Income is statistically significant.

Coefficient of determination = 0.857.
Thus, we can conclude that Work Experience and Level of Education makes up 85.7% of the variance in Annual Income.
The overall fit of the model is significant, and the independent variables (Work Experience and Level of Education) are significant predictors of the dependent variable (Annual Income).