Question

The ANES data below is on age and an ownership index (house + savings + stocks/bonds) for the group classified as “conspiracy theorists.” Is there a relationship between these two variables? By hand or using Excel (Excel is recommended) create a regression equation, calculate r and r² and interpret the results. Then calculate predicted ownership scores for a 25 year old person and an 80 year old person. Show as much work as possible.

Case    Age     Ownership Score

A         42        2

B         62        3

C         62        1

D         67        1

E          37        0

F          47        0

Answer 1

EXCEL is recommended, So i will answer using excel.

First, copy paste the Age and owenership score data in two adjacent columns in Excel

Then select both the columns, go to INSERT, then under Charts tab, click on scatterplot

This scatter plot will be plotted automatically

Right click on any one of the dot plotted on the chart, then select add trendline option

Select linear trendline option and select "Show equation on chart" and "Show R squared value" options.

So, we will get the equation Ownership score = 0.0378(Age) - 0.8324

and coefficient of determination R squared = 0.1615

we know that the coefficient of corrlation (R) = , where R squared = 0.1615

setting the value, we get

Coefficient of correlation R =

Coefficient of correlation R is moderate positive and coefficient of determination is 0.1615, which means that 16.15% variation in the dependent variable can be explained by the model.

Ownership score for 25 years old person, putting x = 25 in the equation, we get

Ownership score = 0.0378(Age) - 0.8324 =0.0378(25) - 0.8324 = 0.9450 - 0.8342 = 0.1126

Ownership score for 80 years old person, putting x = 80 in the equation, we get

Ownership score = 0.0378(Age) - 0.8324 =0.0378(80) - 0.8324 = 3.024 - 0.8342 = 2.1916 or 2.2