# Linear Regression Model

• Mar 2nd 2009, 08:44 AM
statsforcats
Linear Regression Model
Hi, I don't really understand how I go about this problem. I understand regression but I need a little help here.

Question:
Reaction time to a stimulus (y seconds) is believed to be related to the amount of the drug in the bloodstream (x%) by a simple linear regression model where

$E(y) = -0.1 + 0.8x$
and with $\sigma = 0.2$

What proportion of individuals with 4% of the drug in the bloodstream will have a reaction time in excess of 3 seconds?

Well, so far I have substituted in (x = 4) into the equation to get
$E(y) = 3.1$

I'm not sure how to calculate the proportion. Could somebody help me?
• Mar 2nd 2009, 09:03 AM
Ond
Well, one way could be that you have the Y that's normally distributed with mean 3,1 and 0,2 in standard deviation, and you're supposed to find the probability of Y>3?

Am I understaning that correctly? If so, that's a pretty simple problem to solve.
• Mar 2nd 2009, 09:17 AM
statsforcats
Yes that is what I was thinking.
I am wondering now if i get the Probability of Y > 3, is this the same as the proportion >3?

Are Probability and Proportion related?
• Mar 6th 2009, 02:08 PM
statsforcats
Quote:

Originally Posted by Ond
Well, one way could be that you have the Y that's normally distributed with mean 3,1 and 0,2 in standard deviation, and you're supposed to find the probability of Y>3?

Am I understaning that correctly? If so, that's a pretty simple problem to solve.

What type of distribution would this be z, t ?
• Mar 7th 2009, 07:28 AM
Ond
Hi there again.

I think this would be Z since the standard deviation is known, the t-distribution is used when it's unknown.

Regards.