Calculating probability from linear regression parameters

[sadfe]

I'm a bit stuck on how to calculate the probability in part b from the linear regression parameters.
I tried plugging the parameter values into the linear regression model: Y =β0+β1X+ε, ε∼N(0,σ)
So P(Y=y| X=40) = 2.85 + 0.07 * 40 + 1^2
P(Y=y|X=40) = 5.65
But I don't think this is the value I want. Any ideas where I'm going wrong?

 

[mmwave]

Hi there,

It looks like you are on the right track with plugging in the parameter values into the linear regression model. However, the equation you are using is not quite correct. The correct equation for the linear regression model is: Y = β0 + β1X + ε, where ε ~ N(0, σ^2). Notice that the variance, σ^2, is squared, not the standard deviation, σ.

So, the correct equation for calculating the probability would be: P(Y=y| X=40) = β0 + β1(40) + ε, where ε ~ N(0, σ^2). This would give you the probability of Y taking on a specific value, y, when X is equal to 40. You can also use this equation to calculate the probability for a range of values by taking the integral of the normal distribution over that range.

I hope this helps clarify things for you. Let me know if you have any further questions. Good luck with your calculations!