2 if a dependent variable only take values of 0s and 1s eg...

Name: 2 if a dependent variable only take values of 0s and 1s eg whether someoneis employed or not can we assume that the error term in a linear regressionwould be normally distributed what about 71247
Uploaded: 2023-10-13T13:09:36-08:00
Duration: 7 min 18 s
Channel: Adi S
Description: 2 if a dependent variable only take values of 0s and 1s eg whether someoneis employed or not can we assume that the error term in a linear regressionwould be normally distributed what about 71247

2. If a dependent variable only take values of 0s and 1s (e.g., whether someoneis employed or not), can we assume that the error term in a linear regressionwould be normally distributed? What about if the dependent variable takesonly positive or nonnegative values? Explain.

Transcript

00:01 Let's solve this question.

00:02 In this question, we have given that sn cap square that is equals to 1 divided by n minus 2 summation of i is equals to 1 to n yi minus beta 0 cap minus beta 1 cap xi whole square.

00:24 Now here we can see that the linear model that is here yi is equals to beta 0 plus beta 1 xi plus epsilon i where epsilon i that is normally distributed over 0 and sigma square.

00:45 So here we can write beta 0 cap is equals to y bar minus beta 1 cap multiplied by x bar so that implies that beta 1 cap that is equals to sxy divided by sxx that is equals to summation of xi minus x bar multiplied by yi that will be divided by summation of xi minus x bar whole square.

01:13 So here we will get n minus 2 sn cap square that is equals to summation of i is equals to 1 to n yi minus y bar minus beta 1 cap multiplied by x bar minus beta 1 cap xi whole square.

01:35 So that is equals to here we will get summation of i is equals to 1 to n in bracket yi minus y bar minus beta 1 cap multiplied by xi minus x bar whole square.

01:52 So that so that will be equation 1.

01:54 Now here we can write yi minus y bar that is equals to we will get here b1 xi minus x bar plus epsilon i minus epsilon bar.

02:06 So therefore if we put all this value then here we will get yi minus y bar that is equals to epsilon i minus epsilon bar minus beta 1 cap plus beta 1 multiplied by xi minus x bar.

02:27 So this will be suppose equation 2.

02:30 Now here we can write n minus 2 s bar square that is equals to summation of i is equals to 1 to n yi minus y bar minus beta 1 cap multiplied by xi minus x bar whole square.

02:50 Here we will put the equation value here so that is equals to here we will get summation of i is equals to 1 to n epsilon i minus epsilon bar minus beta 1 cap minus beta 1 multiplied by xi minus x bar whole square...

Question

2. If a dependent variable only take values of 0s and 1s (e.g., whether someoneis employed or not), can we assume that the error term in a linear regressionwould be normally distributed? What about if the dependent variable takesonly positive or nonnegative values? Explain.

Please give Ace some feedback