Ask Question, Ask an Expert


Ask Statistics and Probability Expert

Show all your work.
1. The following sample on the level of education (measured by the number of years of schooling) and wages (hourly) earned by 15 individuals is as follows:

Education    Wages ($)        Education         Wages ($)
6                  4.45                 10                 7.31
7                  5.57                 12                  7.82
8                  5.97                 14                 11.02
9                  7.33                 15                 10.67
10                7.31                 16                 10.83
11                6.58                 17                 13.61
6                 4.45                  15                10.67
18              13.53

According to the human capital theory education increases a worker’s productivity and thus leads to higher wages. Consider the economic model Wages β0 + β1 Education.

a. What sign would you expect β0 and β1 to take? Draw a rough scatter graph of the data with wages on the vertical axis and education on the horizontal axis. Does it look like the data support the human capital theory?

b. Estimate Wages β0 + β1Education + u. Give a plot of Wagesi. Interpret the intercept and the slope coefficient.

c. find out the standard error of β0 and β1

d. find out the 99% confidence interval for β0 and β1.

e. Test the null hypothesis β1 = 0 at 1% level of significance.

f. find out and interpret R2

g. describe the assumption of homoscedasticity.

2. Under the OLS estimation the following hold:

∑ ui = 0, ∑ uiXi = 0, and ∑ ui Yi = 0.

Prove and describe the above properties.

3. Show that the OLS estimate of β0 and β1  is unbiased

4. Prove that the cov (β0, β1) =−X σ2/∑xi2

5. For the following model derive the least square estimator of α, Y = α + u

Show that the OLS estimator for α is BLUE under Gauss Markov Assumptions.

Which assumption is important for the estimator to be unbiased?

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M9982
  • Price:- $35

Guranteed 24 Hours Delivery, In Price:- $35

Have any Question? 

Related Questions in Statistics and Probability

After gaining an understanding from the video on secondary

After gaining an understanding from the video on secondary data, provide at least two public websites where we can get data for research. Here's one example. We can pull the unemployment rate for each state from the bure ...

A three-dimensional vector random variable x has a

A three-dimensional vector random variable, X, has a covariance matrix of Find a transformation matrix A such that the new random variable   Will be uncorrelated.

According to figures released by the new york city

According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago (The New York Times, January 2, 2008). According ...

Question 1visit the australian stock exchange website

Question 1: Visit the Australian Stock Exchange website, and from "Prices and research" drop-down menu, select "Company information". Type in the ASX code "WPL" (Woodside Petroleum Limited), and find out d ...

You are given a member function of a random process

You are given a member function of a random process as   where the amplitude is in volts. Quantize the amplitude o    to 21 levels with the intervals ranging from 10.5 to 10.5 in 1-volt steps. Consider 100 periods of   a ...

Consider a modified version of the experiment in example

Consider a modified version of the experiment in Example where we flip a coin until the first occurence of tails or until we flip the coin four times, whichever comes first. (a) List the possible outcomes of this experim ...

Suppose x is a vector of iid random variables where each

Suppose X is a vector of IID random variables where each element has some PDF,    Find an example PDF such that the median is a better estimate of the mean than the sample mean.

Question nbspproblem consists of two different scenarios

Question : Problem consists of two different scenarios requiring you to find the market demand curve. a.  Joe, Mary, and Ellen all have the same individual demand curve for peanuts. This demand curve is P = 10 - Q. They ...

Sat verbal scores are normally distributed with a mean of

SAT verbal scores are normally distributed, with a mean of 500 and standard deviation of 100. You randomly select a test taker. What's the probability that s/he scored between 500 and 700?

Two balls are selected sequentially without replacement

Two balls are selected sequentially (without replacement) from an urn containing three red, four white, and five blue balls. (a) What is the probability that the first is red and the second blue? (b) What is the probabil ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate