Stat

STAT 2103 Project 4:

Performing a Multiple Linear Regression Analysis

Goal: Use the data set provided and the statistical methods learned in class to carry out an

applied multiple linear regression analysis.

Data: The data set for this project has been posted to Blackboard. The observational units in the

sample are 146 countries. The response variable (Y) is a “HAPPY”, an index of each country’s

overall happiness. Also included are 10 predictor variables (X’s), such as GDP, life expectancy,

health care expenditure, and population density. The “Description” tab explains each variable.

Method: You can complete the regression using StatCrunch (recommended) or Excel:

 StatCrunch: On MyStatLab, select “StatCrunch”, then “StatCrunch website”, then “Type

or paste data into a blank data table”. Then use the “Stat” menu, “Regression”, and

“Multiple Linear”. Choose the correct variables and specifications.

 Excel: Download “Analysis ToolPak” add-in (File – Options – Add-Ins – Manage). Then

“Data Analysis”, select “Regression”. Choose the correct input and specifications.

Assignment: Perform a multiple linear regression analysis. This includes:

 List Variables: Select and list 4 predictor variables that you think may be related to

happiness.

 Explore Variables: Include a scatterplot of the response variable “HAPPY” on the y-axis

and one of your predictor variables on the x-axis. Describe their relationship/correlation.

 Write Model: Construct and write out a multiple linear regression model with your

selected variables.

 Analyze Model: Use the statistical output to identify which predictor variables are

significantly important and how much of the variability in the response variable is

explained (the r 2 value).

 Finalize Model: Rerun the regression model using only the significant predictor variables.

(If none were significant the first time, use the two variables with the lowest p-values.)

 Learn from Model: Choose one variable from this finalized model and interpret its

coefficient. Also, why do you think that the r 2 is so high or so low?

 Predict with Model: Select a country from the sample. Use the values of that country’s

predictor variables and the final regression model to estimate that country’s HAPPY

index. Find how much the model overestimated or underestimated the true value.

Details: Due date is in class on Thursday, December 4. The previous class on Tuesday,

December 2 will be partially spent as an in-class work day for the project, so it is recommended

that you bring your laptop to class that day if you have questions.