## Solved – Dealing with a categorical variable that can take multiple levels simultaneously

I recently posted a question with many parts and I'd like to focus in on just one issue that I didn't emphasize in the original post. My data is a list of records, each one representing an educational seminar event. I have a continuous variable that represents the revenue brought in by each seminar, which … Read more

## Solved – Explained Sums of Squares in matrix notation

I am currently reading Appendix C from Gujarati Basic Econometrics 5e. It deals with the Matrix Approach to Linear Regression Model. I am unable to decipher how the author went from equation 7.4.19 to C.3.17 Best Answer In short, the author is not going from 7.4.19 to C.3.17. C.3.17 is just a definition, from which … Read more

## Solved – Does the \$R^2\$ depend on sample size

It's well known that adding more regressors can only improve the \$R^2\$. What about the number of observations? Say you have a sample of size \$N\$, and you draw a random subsample of size \$n < N\$. How should, in principle, the \$R^2\$ change? Two things are fairly intuitive: The closer the subsample size to … Read more

## Solved – Does the \$R^2\$ depend on sample size

It's well known that adding more regressors can only improve the \$R^2\$. What about the number of observations? Say you have a sample of size \$N\$, and you draw a random subsample of size \$n < N\$. How should, in principle, the \$R^2\$ change? Two things are fairly intuitive: The closer the subsample size to … Read more

## Solved – Fit multiple regression model with pairwise deletion (or on a correlation/covariance matrix) in R

I'm trying to fit a multiple regression model with pairwise deletion in the context of missing data. lm() uses listwise deletion, which I'd prefer not to use in my case. I'd also prefer not to use multiple imputation or FIML. How can I do multiple regression with pairwise deletion in R? I have tried the … Read more

## Solved – Fit multiple regression model with pairwise deletion (or on a correlation/covariance matrix) in R

I'm trying to fit a multiple regression model with pairwise deletion in the context of missing data. lm() uses listwise deletion, which I'd prefer not to use in my case. I'd also prefer not to use multiple imputation or FIML. How can I do multiple regression with pairwise deletion in R? I have tried the … Read more

## Solved – How to justify the choice of independent variables in multiple regression

I am trying to measure the effect of atmospheric factors as smell or light (IV) on purchase behavior (DV). In total I have xx likert scales that contain 5 likert items and responses are coded from 1 to 5. I am wondering which approach would be the best to show that my IVs have some … Read more

## Solved – Does it make sense for p-value to decrease with more data points

I'm running a multiple linear regression on a set of sports data. When I run the regression on one season, which has 380 data points and which I thought was a fair amount, I get quite a high p-value on one of my independent variables. However, when I run the regression on all my data … Read more

## Solved – How to interpret Residuals vs. Fitted Plot

I am investigating the effects of weather on restaurant demand. Currently, I am testing the model assumptions for my multiple linear regression model. My model specification (simplified) is as follows: lm(Visitor ~ Temperature + Temperature_Squared + Pressure + Clouds + Sun + Rain + Day_Fri + Day_Sat + Day_Sun + Day_Mon + Day_Tue + Day_Wed … Read more

## Solved – Can Adjusted R squared be equal to 1

I have a dataset with around 15 independent variables. I am using a multi-regression model to fit the dataset. For model selection, I am using a backward elimination procedure based on the p-values. The adjusted R^2 for the model with all predictors is exactly 1. At this point, I concluded that maybe the model is … Read more