Question

What is the difference between the following two regression​ equations? ModifyingAbove y with caret equals b 0 plus b 1 xy=b0+b1x y equals beta 0 plus beta 1 xy=β0+β1x Choose the correct answer below. A. The first equation is for sample​ data; the second equation is for a population. B. The first equation is for a​ population; the second equation is for sample data.

Answer 1

Answer:

A. The first equation is for sample​ data; the second equation is for a population.

Step-by-step explanation:

The first equation is y = $b_0 + b_1x$ , this is the equation for sample data as the intercept ($b_0$) and the slope parameter($b_1$)  both are calculated then we have got this and these values are not taken as given.

The Second equation is $y = \beta _0 +\beta _1x$ , this is the equation for population data as we can't calculate these $\beta _0$ and $\beta _1$ as we take these values as given and also we do testing for $\beta$ parameter using t test and it is sure that testing is always done on population data not on sample data.

Answer 2

The true statement is (b) the first equation is for a​ population; the second equation is for sample data.

The equations are given as:

$\mathbf{\^y = b_0 + b_1x}$

$\mathbf{\^y = \beta_0 + \beta_1x}$

In regression, $\mathbf{\beta}$ is used as an estimator of an actual population.

This means that:

Sample $\mathbf{\beta}$ is an estimator of population, b

So, we can conclude that:

The first equation represents population, while the second represents sample

Hence, option (b) is correct

Read more about regression equations at:

https://brainly.com/question/16438646