Econometrics Foundations Assignment

What is the summation of the monthly incomes for Ali, Faisal, Iqbal, and Noreen using the formula ∑?

For the linear function $Y = 5 + 2X$, what is the value of Y when X = 3?

For the quadratic function $Y = 2X^2 + 3X + 5$, what value of X results in the lowest point of the graph?

What is the trend value for Y, given the data points for Y, when X = 7 in a simple linear regression?

What is the value of the partial derivative $\frac{\partial Z}{\partial Y}$ for the function $Z = 2X^2 + 3Y^2 + 5XY$?

Assignment Instructions

This is an individual assignment focused on econometric foundations.
All answers must show all steps and be detailed/clear.
No appendices are allowed.
Use appropriate graphs, formulas, and explanations.
Use a typed format (Word).

Task 1

Calculate the total monthly income of individuals (Ali, Faisal, Iqbal, Noreen) using summation notation.
The provided monthly incomes are: Ali (75000), Faisal (42000), Iqbal (33000), Noreen (65000).

Task 2

The linear function is Y = 5 + 2X.
Determine Y values for X = 1, 2, 3, 4, and 5.
Plot these points on a graph and draw a line representing the function.

Task 3

The quadratic function is Y = 2X² + 3X + 5.
Calculate Y values for X = -2, -1, 0, 1, and 2.
Plot these points on a graph and determine whether the graph represents a maximum or minimum.

Task 4

Estimate a linear regression Y on X using the given data points.
Calculate trend values and errors.
A table of X and corresponding Y values is given for regression analysis.

Task 5

The given function is Z = 2X² + 3Y² + 5XY.
Calculate the partial derivatives ∂Z/∂X and ∂Z/∂Y.
Show all steps in the calculation.

This assignment covers various tasks related to econometrics fundamentals, including calculating total monthly income using summation notation, analyzing linear and quadratic functions, and estimating linear regression. Students will display their calculations, graphs, and interpretations clearly and in detail.