The following model was fitted to data on 32 insurance...

The following model was fitted to data on 32 insurance companies: where y' = price-earnings ratio x1 = size of insurance company assets, in billions of dollars x2 = dummy variable taking the value 1 for regional companies and 0 for national companies The numbers in parentheses under the coefficients are the estimated coefficient standard errors. a. Interpret the estimated coefficient on the dummy variable. b. Test against a two-sided alternative, the null hypothesis that the true coefficient on the dummy variable is 0. c. Test, at the 5% level, the null hypothesis β1 = β2 = 0, and interpret your result.

Transcript

00:01 So we've got a model where we've got three variables we're looking at.

00:04 We have 1, which is y, the response variable, is the price -to -earnings ratio.

00:14 And we have x1, which is the size of insurance company assets and billions of dollars.

00:20 And then x2, it's a dummy variable.

00:43 It's whether or not it's regional or national companies.

00:46 These regional where it's a one if it's a regional and zero if it's a national company.

01:00 And so the model would look like this.

01:02 Y hat is equal to beta naught hat plus beta one hat x1 plus beta two hat x2.

01:14 And then we have some numbers in parentheses under the coefficients.

01:21 Now we're not given those, but that's okay.

01:22 So underneath them you'd see the this is the coefficient standard error.

01:27 So it's your standard error of that certain coefficient.

01:35 Sv beta hat one and then sv beta hat two.

01:41 Something like that.

01:42 And it would be some number.

01:43 We're not given the numbers, but that's okay.

01:45 The first thing we're going to do is interpret the coefficient on the dummy variable right here so whatever the number is if it's remember if it's a one it's regional if it's zero it's national what this means is that whatever it is if you if you put a 1 and for x 2 if x 2 is equal to 1 that means you add beta hat 2 to your that actual value whatever that value is to your your output and that's going to give you the you're adding to the price per earnings ratio so that means if it's a one you add this if it's if x2 is a zero that means the model itself is built on being national that means the model is built on national is built with national national as like your base, the base case.

02:56 And then when you put a one, you incorporate this.

03:00 That makes it regional.

03:02 That's a if we interpret that.

03:03 So it's the amount you add or subtract if it's negative to get your price per earnings ratio.

03:08 For part b, we're going to test a two -sided alternative that the null hypothesis is true, that the null hypothesis that the coefficient of the dummy variable is zero.

03:16 So i have this here...

Question

Please give Ace some feedback