# Does linear regression make inferences about a population from sample data?

#### sampier85

##### New Member
In psychology we usually collect samples because we do not have access to the entire population. Given this, is regression an inferential technique...for example if i ran a linear regression model on the effect of impulsivity and aggression on the number of car accidents (Just an example!) based on a sample of 50 people, does SPSS provide me with population level estimates or just analysis based on my sample?

Could you also guide me to the theory behind it?

#### NN_STAT

##### New Member
regression is a model that uses inferential tools. when SPSS estimate the coefficients of the regression (what is called beta's in SPSS) it is doing hypothesis testing, which is inferential.

you start with a sample, you calculate the coefficients, and then you can take values from the population, call them X1 and X2, and you can predict the value of Y knowing these values. but be ware, you can only make predictions in the range you had in the sample.

#### SiBorg

##### New Member
does SPSS provide me with population level estimates or just analysis based on my sample?
I'd be a little bit wary about that statement. As far as I know, statistical inference calculates the uncertainty in the estimates but that is based on the underlying variance in your data. Therefore, it gives you some idea about the likely range of values in a population identical in variance to your own population but you should be careful about applying this to the 'population at large' unless you are fairly sure that your population has been selected with no bias.

But, as NN_STAT says, SPSS will give you p values and confidence intervals which are inferential.

#### trinker

##### ggplot2orBust
SiBorg is spot on, high quality statistical procedures don't make up for design issues. If you didn't randomly sample and randomly assign grouping then you really can't (IMHO) make any inference about the population. Also be careful of what the population is. If you sampled from homicidal robots then your inference is about the population of robots (I dropped homicidal because it's redundant to say it).