Question

- Explain the limitations of the linear regression model. [5 marks]
- Using a sample of 1801 employees, the following earning
equation has been estimated:

(0.135) (0.008) (0.007) (0.036)

Where:

Y is earnings, x_{1} is education level,x_{2} is
experience and x_{3} is female

The standard errors are the values in brackets.

R^{2}=0.179

Required:

- Interpret each of the coefficient estimates. [5 marks]
- At 5% significance level, test the hypothesis that there is no difference in expected earnings between male and female employees. [5 marks]

Answer #1

(a) Linear regressions are sensitive to outliers.

It is easy to overfit your model such that your regression begins to model the random error (noise) in the data, rather than just the relationship between the variables.

Linear regressions are meant to describe linear relationships between variables. So, if there is a nonlinear relationship, then you will have a bad model.

(b) (i) For every addition in education level, the earnings will increase by 0.008.

For every addition in experience, the earnings will increase by 0.007.

For every female, the earnings will increase by 0.036.

(ii) The data is missing.

Using data from 50 workers, a labour economist runs a multiple
regression of Y (hourly wage in $) on X1 (years of education), X2
(gender) and X3 (an interaction between X1 and X2), and obtains the
following regression results.
Coefficients
Standard error
Intercept
-16.78
2.14
Years of education
2.77
0.16
Gender (coded 1 for female and 0 for
male)
8.84
3.01
Interaction between years of education and
gender
-1.02
0.22
Based on the above information, the estimated effect of X1...

We have used the 1987 baseball salary data to illustrate linear
regression. In this project, we consider
the 1992 baseball salary data set, which is available from
http://www.amstat.org/publications/jse/datasets/baseball.dat.txt
This data set (of dimension 337 × 18 ) contains salary
information (and performance measures) of
337 Major League Baseball players in 1992. More detailed
information can be found at
http://www.amstat.org/publications/jse/datasets/baseball.txt
The data set contains the following variables.
Table 1: Variable Description for the 1992 Baseball Salary
Data
Var Columns Description
salary...

1. In a multiple
regression model, the following coefficients were obtained:
b0 = -10 b1
= 4.5 b2 = -6.0
a. Write the
equation of the estimated multiple regression model. (3 pts)
b Suppose a
sample of 25 observations produces this result, SSE = 480. What is
the estimated standard error of the estimate? (5 pts)
2. Consider the
following estimated sample regression equation:
Y = 12 + 6X1 -- 3 X2
Determine which of the following
statements are true,...

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