Quantitative Business Analysis: Regression Analysis of Hourly Earnings

This assignment focuses on quantitative business analysis, specifically employing regression analysis to understand and predict hourly earnings. The analysis begins with a simple regression of hourly earnings on age, revealing a positive correlation. Further analysis incorporates gender and education as additional variables, leading to a multiple regression model. The assignment then compares the outcomes of these different models, highlighting the impact of omitted variable bias. Using the regression results, the assignment predicts earnings for individuals with specific characteristics and examines the differences in R-squared values between the models. The analysis also explores the impact of removing certain variables, such as gender and education, from the regression model, and how this affects the slope of age. The assignment provides detailed tables and statistical outputs to support the analysis, demonstrating the application of regression analysis in real-world scenarios, and demonstrating how different variables impact the final outcomes.

Quantitative
Business : Question
C

TABLE OF CONTENTS
QUESTION C..................................................................................................................................3
C1 Regression on hour earning on age........................................................................................3
C2 Running regression of AHE on age, gender and education...................................................4
C3 Difference from the outcome of C1 and C2...........................................................................5
C4 Predicting earning using regression.......................................................................................5
C5 ................................................................................................................................................5
C6.................................................................................................................................................5
C7.................................................................................................................................................7

QUESTION C
C1 Regression on hour earning on age
In the below mentioned table, regression has been found with the average hourly earning
and age. It has been found that regression of age on average hourly earning is .561. This reflects
the values of earning changes with respect to age. For example, those with the higher age group
might have good earning in comparison to those who have recently joined the job. In this
manner, outcome differs in accordance with the age.
a. Dependent Variable: Average Hourly Earnings
b. The independent variable or constant was the age factor

Slope=.561
AHE=.561 (age)+2.763
C2 Running regression of AHE on age, gender and education
a. Dependent Variable: Average Hourly Earnings
b. The Age and Gender are considered as the predictor in the above calculation
The calculation has been presented as follows which aids to derive the exact value.
AHE+.549*(age)-3.742*gender+8.217*education+.566

C3 Difference from the outcome of C1 and C2
The regression applied in case of C1 has one variable as age with AHE however, in case
of C2 AHE has been compared with three variables such as age, gender and education. Owing to
this, the value of age is .549 in multiple regression which was higher in C1. Thus, values or
regression under C1 seem to suffer form omitted variables bias.
C4 Predicting earning using regression
The predication has been done in accordance with the above mentioned table so as to find
the best outcome and value related to AHE in case of BOB AND Alexis both.
In case of Bob
AHE=.549*26+.566=14.84
In case of Alexis
AHE=.551*30+7.686=24.216
C5
There is significant difference in the R square in the C1 and C2 as the application of
variable was different in the both cases. It is because in case of C1 researcher applied only on
variable where under the C2 both variables are used.
C6
If female can be deleted
a. Dependent Variable: Average Hourly Earnings
b. Education and Age both are the estimator in context of constant

If bachelor can be deleted from the regression
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 62836.894 2 31418.447 300.857 .000b
Residual 1581901.547 15148 104.430
Total 1644738.441 15150
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 4.161 .872 4.771 .000
Age .551 .029 .151 18.891 .000
Gender -2.552 .168 -.121 -15.205 .000
If female and bachelor can be deleted
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 38693.566 1 38693.566 364.977 .000b
Residual 1606044.874 15149 106.017

Total 1644738.441 15150
a. Dependent Variable: Average Hourly Earnings
b. Predictors: (Constant), Age
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 2.763 .874 3.162 .002
Age .561 .029 .153 19.104 .000
In the manner value of regression for each variable is different in all cases. Therefore, multiple
regression has significant impact on the final outcome.
C7
As per the last condition of C5 it can be understood that slope of age is .561 when both
bachelor and female are deleted. However, otherwise it was different in mentioned above
condition.