Linear Regression Model

[Guest]

A research team is studying cognitive decline in old age. They collect data on 300 people between the ages of 75 and 95 years. One of the key variables is a measure of one particular aspect of cognitive functioning: Executive function (named EXFUNC in the dataset). For this study it is measured using a test that produces values ranging from 0 to 100, with higher values representing better executive function. The investigators fit a linear regression model to their data and obtain the following estimated model:

EXFUNCi = 161.73 – 1.05AGEi + ei

According to this model, by how many points does the typical score on the executive function scale decline between age 80 and 90?

[HallsofIvy]

Really? When I saw the title, I thought this would be about how to find the linear regression given some data. However, here you are told that y= 161.3 – 1.05x+ ei where "x" is the age (your AGEi) and y is the "executive functioning" (your EXFUNCi).

So what is y when x= 75? What is y when x= 80? Those will both be a specific number plus the unknown "ei" but to get the "decline" you need to subtract and the constant "ei" will cancel.

[HallsofIvy]

Really? When I saw the title, I thought this would be about how to find the linear regression given some data. However, here you are told that y= 161.3 – 1.05x+ ei where "x" is the age (your AGEi) and y is the "executive functioning" (your EXFUNCi).

So what is y when x= 75? What is y when x= 80? Those will both be a specific number plus the unknown "ei" but to get the "decline" you need to subtract and the constant "ei" will cancel.