Quiz: Interpreting Coefficients in MLR

Interpreting Coefficients Attached to Quantitative Variables

We are now moving into material that combines math, code, and the real world. It is important to make sure we have all of the basics down before we jump into coding problems.

QUIZ QUESTION::

Consider we are predicting the price of a stock based on the accounting information of a company. Drag the type of each variable next to the variable name.

ANSWER CHOICES:

Name	Type
Number of Employees
Country Location of Headquarters
Industry of the Company
Price of All Assets

SOLUTION:

Name	Type
Country Location of Headquarters
Industry of the Company
Country Location of Headquarters
Industry of the Company
Number of Employees
Price of All Assets
Country Location of Headquarters
Industry of the Company
Number of Employees
Price of All Assets
Number of Employees
Price of All Assets
Country Location of Headquarters
Industry of the Company
Number of Employees
Price of All Assets

Now imagine…

We build a linear model using the above four aspects to predict the stock price of each company, which variables can you add based on what you have learned so far?

SOLUTION:

Number of Employees
Price of All Assets

Now imagine…

We fit a multiple linear regression model using the x_1, number of employees, and the x_2, price of all assets, to predict y, the price of the stock.

We obtain a linear model of the form:

\hat{y} = b_0 + b_1x_1 + b_2x_2

where:

b_0 = -3.20
b_1 = 0.60
b_2 = 0.24

Use this information to answer the quiz questions below.

Based on the results of your multiple linear regression model, which of the below would be correct interpretations? Mark all that apply.

If a company has no employees and no assets, we predict they have a stock price of -3.20.

For each additional employee a company adds, we predict an increase in stock price by 0.60 if the amount in assets remains the same.

For each unit increase in assets, we predict an increase in stock price by 0.24 if the number of employees stays constant.

We could continue to add variables to this model, and the interpretation of these coefficients would basically stay the same, but we would add more variables to the "held constant" portion of the interpretation.

SOLUTION:

If a company has no employees and no assets, we predict they have a stock price of -3.20.
For each additional employee a company adds, we predict an increase in stock price by 0.60 if the amount in assets remains the same.
For each unit increase in assets, we predict an increase in stock price by 0.24 if the number of employees stays constant.
We could continue to add variables to this model, and the interpretation of these coefficients would basically stay the same, but we would add more variables to the "held constant" portion of the interpretation.