# Multiple regression model and prediction/confidence interval for two values of a coefficient

Hi i've been working on this model of house prices based on multiple independent variables. I got the out put out throught gretl. https://www.dropbox.com/s/sq1oryrjhmplsgx/Screen%20Shot%202015-05-15%20at%206.01.02%20am.png?dl=0

Now i'm trying to interpret this additional question that got me confused... "Consider two houses that have the same size, same baths, same stories and same number of garages but one is two beds and the other is five beds. How much difference in the prices should an investor expect between the two houses according to model 1? Construct a 95% confidence interval for this difference in the prices and interpret your result."

I presume this means that the difference of 3 room equates to a difference of price equal to 3 times the coefficient of $\beta_3$ "Beds" which is $$3\times2388.49 =7165.47$$

I get lost at the concept of a 95% confidence interval for a multiple regression without giving the quantity x values for variables!

Now i'm going to get here that the confidence interval is "the difference $\pm$ se(Beds)*$t_{460,0.05/2}$

Where $$t_{460,0.05/2}=1.96482$$

So confidence interval is $7165.47 \mp 1184.23(1.96482)$ $$CI: 4838.6712,9492.2688$$

• Can you provide the entire model that was fit? At least the formula ... – Eric Farng May 15 '15 at 2:39
• It's on the link – Ivan May 15 '15 at 3:13