Comprehensive Guide to Multiple Regression Analysis and Model Interpretation

What is the primary advantage of multiple linear regression over simple linear regression?

It allows multiple explanatory variables and controls for other factors.

In a multiple regression model, how is a slope coefficient interpreted?

The average change in Y for a one-unit increase in X while holding all other variables constant.

Why might customer size be included in a revenue model that uses call minutes?

To separate the effect of call minutes from customer size.

What does a decreased coefficient for call minutes after adding customer size imply?

Customer size was explaining some of the relationship previously attributed to call minutes.

What is a true statement about residual plots?

Residuals should appear randomly scattered.

Which is NOT a reason to add another variable to a regression model?

It exists in the dataset.

What happens to R² when a new variable is added?

Always increases or stays the same.

What happens to Adjusted R² when an irrelevant variable is added?

Often decreases.

Which measure is generally better for comparing regression models with different numbers of variables?

Adjusted R².

Which regression model is likely best based on R² and Adjusted R² values?

Model B.

How many dummy variables are needed for a variable with 4 categories?

3.

How many dummy variables are needed for a variable with 6 categories?

5.

What is the category that is absorbed into the intercept called?

Baseline/reference category.

If Healthcare is the baseline industry, what does the coefficient for Technology represent?

Technology compared to Healthcare.

Which of the following is a binary categorical variable?

Existing customer (Yes/No).

Does statistical significance automatically mean the model is useful?

False.

Can patterns in residuals indicate problems with a model?

True.

Can multiple regression use both numerical and categorical explanatory variables?

True.

Can Adjusted R² decrease when a variable is added?

True.

Can R² decrease when a variable is added?

False.

Do model predictions change when the baseline category changes?

False.

Does changing the baseline category change the interpretation of coefficients?

True.

If a categorical variable has k categories, how many dummy variables do you need?

False.

In multiple regression, how is every slope interpreted?

While holding the other variables constant.

What does a regression coefficient for Customer Size of 50 mean?

Revenue increases by $50 for every $1,000 increase in customer spending, holding other variables constant.

What does a coefficient for Existing Customer = 1200 mean?

Existing customers generate $1,200 more revenue than new customers on average, holding other variables constant.

Why do statisticians use control variables?

To separate the effects of different variables.

What does a U-shaped pattern in residuals indicate?

The linear model may be inappropriate.

What best describes multiple regression?

It estimates one numerical outcome using multiple explanatory variables.