Question

Question 1:

Consider the simple regression model: !Yi = β0 + β1Xi + ei
(a) Explain how the Ordinary Least Squares (OLS) estimator formulas for !β̂ and !β̂ are derived.

2. (b) Under the Classical Linear Regression Model assumptions, the ordinary least squares estimator, OLS estimators are the “Best Linear Unbiased Estimators (B.L.U.E.).” Explain.

3. (c) Other things equal, the standard error of β! ̂ will decline as the sample size increases. Explain the

   importance of this.

Question 2:

Consider the following data on 10 students:

1

01

Observation Weekly Food Expenditure Weekly Income
1	80	200
2	70	100
3	60	80
4	80	220
5	100	230
6	70	160
7	50	60
8	70	80
9	70	130
10	80	140

(a) Calculate the values of !β ̂ and β! ̂ for the simple linear regression model given by: 01

!food =β̂ +β̂income +e. i01 ii

2. (b) Interpret those values in the context of the variable definitions and units of measurement.

3. (c) Using the results from part (a), calculate the error (e! i) for each of the 10 observations.

(c) Calculate and interpret the standard error of tĥe regression (!se).

(d) Calculate and interpret the standard error of the β! ̂ estimate (!s ). 1β̂

(e) Test the null hypothesis that income has no effect on food expenditures. What do you conclude?

Answer 1

STEP 1:

Paste the data in MS-Excel

STEP 2:

Go to Data > Data Analysis > Regression

STEP:3

Select the range of X variable and Y variable , and tick the required result > Press apply button

You will get the explained details all that you need in the question as:

FOR BETTER UNDERSTANDING OF THE TABLE, REFER TO THE FOLLOWING TABLE: