Question

Suppose the line of best fit for some data points has a slope of 1.581. If the mean of the x-coordinates of the data points is 5.923, and the mean of the y-coordinates is 12.478, what is the y-intercept of the line to three decimal places?

A. 13.805
B. -3.114
C. -13.805
D. 3.114

Answer 1

3.114 (apex VERIFIED)

Answer 2

`\hat \beta_0 = 12.478 - 1.581 *5.923= 3.114`

So then the best answer is:

D. 3.114

Explanation:

For this case we have a linear model given by:

`y = \beta_1 x + \beta_0`

Where
`\hat \beta_1 = 1.581`

And we ar einterested on find the value for
`\beta_0` assuming that we have the following coordinates (x= 5.923 , y = 12.478) we cna solve for the desired value like this:

`\hat \beta_0 = \bar y -\hat \beta_1 \bar x` that result comes from the maximum estimation likehood of the parameters.

And if we replace the values we got:

`\hat \beta_0 = 12.478 - 1.581 *5.923= 3.114`

So then the best answer is:

D. 3.114