Understanding Correlation in Economics

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Questions and Answers

What is indicated by a negative correlation between two variables?

Both variables vary independently of each other

There is no relationship between the two variables

An increase in one variable leads to a decrease in the other (correct)

An increase in one variable leads to an increase in the other

Which of the following best defines a non-correlated relationship?

An increase in one variable results in an increase in the other

A direct proportionality between two variables

A relationship where one variable affects another

There exists no relationship between the two variables (correct)

What does the correlation coefficient, denoted by r, measure?

The mean of the two variables

The total number of data points

The degree of linear association between two variables (correct)

The variance of the dataset

What does the regression line of x on y indicate about the relationship between x and y?

It predicts x based on y. Signup and view all the answers

When is it necessary to use more complex measures of correlation?

When a linear relationship is insufficient to describe the data Signup and view all the answers

When the correlation coefficient r equals zero, what can be inferred about the regression lines?

They are perpendicular to each other. Signup and view all the answers

Which of the following is true about the correlation coefficient's numerical limits?

It can take values only in the range [-1, 1] Signup and view all the answers

What type of diagram is used to plot the values of two variables in order to visualize their relationship?

Dot diagram or scatter diagram Signup and view all the answers

What does the coefficient of correlation represent in relation to the coefficients of regression?

It is the geometric mean of the regression coefficients. Signup and view all the answers

In the context of correlation analysis, what does it mean if the coefficient of correlation is close to +1?

A strong positive relationship Signup and view all the answers

If both coefficients of regression are positive, what can be said about the correlation coefficient?

It is positive. Signup and view all the answers

Which formula is used to compute the correlation coefficient between two variables x and y?

$rac{ ext{Cov}(x,y)}{ ext{std}(x) ext{std}(y)}$ Signup and view all the answers

What is true about the means of x and y in relation to their regression lines?

They lie on both regression lines. Signup and view all the answers

What indicates a perfect correlation between two variables in regression analysis?

The regression lines coincide. Signup and view all the answers

What can be said about the angle between the regression lines when the correlation coefficient is one?

The angle is acute. Signup and view all the answers

What is represented by the symbols $\bar{x}$ and $\bar{y}$ in regression analysis?

The means of x and y. Signup and view all the answers

What is the equation of the line of regression of y on x?

y = 0.0851x - 1.2536 Signup and view all the answers

What value of x is obtained when y is equal to 5 in the regression of x on y?

72.213 Signup and view all the answers

In the context of multiple regression, what does the model y = β0 + β1 X1 + β2 X2 + ... + βk Xk represent?

A multiple linear regression model Signup and view all the answers

Which of the following best describes a multiple regression model?

Uses multiple independent variables to predict a dependent variable. Signup and view all the answers

What does β0 represent in the multiple linear regression model?

The intercept of the regression line Signup and view all the answers

When conducting a multiple linear regression analysis, what is assumed about the n-tuples of observations?

They follow the same regression model structure. Signup and view all the answers

What is the purpose of using multiple regression analysis?

To predict values of a dependent variable based on multiple independent variables. Signup and view all the answers

What is the relationship shown in the equations provided for y1, y2,..., yn?

Multiple explanatory variables affect each observed response value. Signup and view all the answers

What does the least squares principle aim to minimize in the context of fitting a multilinear model?

The sum of the squared differences between observed and predicted values Signup and view all the answers

In a multilinear model, if the sales of items A and B are both predictors, what is typically being predicted?

The profit made by the company Signup and view all the answers

Which of the following best describes the form of the normal equations derived from the least squares principle?

They include terms for both sales of item A and item B multiplied by unknown coefficients. Signup and view all the answers

When fitting a multilinear model, what is the significance of solving the normal equations?

To find the coefficients that best represent the relationship between variables. Signup and view all the answers

In the given example, what factor should be taken into account while fitting the multilinear model?

The interaction between sales of item A and item B. Signup and view all the answers

What is the purpose of the given normal equations?

To determine coefficients for a regression equation Signup and view all the answers

Which variables are involved in the regression equation presented?

Oven width and flue temperature Signup and view all the answers

What is the total sum of the first column of the provided data?

59 Signup and view all the answers

What statistical concept do the normal equations relate to in this context?

Linear regression analysis Signup and view all the answers

From the data, which value corresponds to the sum of the second column?

24 Signup and view all the answers

Study Notes

Demand and Price of a Commodity

An increase in price leads to a decrease in demand, and vice versa.
This is an example of a negative correlation.

Income and Expenditure

An increase in income often leads to an increase in expenditure, and vice versa.
This is an example of a positive correlation.

Negative Correlation

When an increase in one variable causes a decrease in another variable, or vice versa.
Examples include:
- Supply and Price of a commodity
- Volume and pressure of a perfect gas

No Correlation

When there is no relationship between two variables, there is no correlation.

Scatter Diagram

A visual representation of data points showing the relationship between two variables (x and y).
It helps understand the nature of correlation.

Correlation Coefficient

Denoted by 'r,' it measures the degree of linear association between two variables.
Values range from -1 to 1:
- 1 indicates a perfect positive correlation
- -1 indicates a perfect negative correlation
- 0 indicates no correlation

Regression Line

A line that represents the best fit for the relationship between two variables.
There are two types:
- Regression line of x on y: predicts x based on y
- Regression line of y on x: predicts y based on x

Properties of Lines of Regression

The lines intersect at the mean of x ( ̄ ) and the mean of y ( ̄ ).
The angle between them depends on the correlation coefficient (r):
- When r = 0 (no correlation), the lines are perpendicular.
- When r = 1 or -1 (perfect correlation), the lines coincide.

Multivariate Regression Analysis

Uses multiple independent variables to predict a dependent variable.
An extension of simple linear regression.
The model uses least squares estimation to find the best fit.

Example:

A company produces two items (A and B).
Data includes sales of each item and profit for each day.
The aim is to find a multilinear model that relates sales of A and B to profit using least squares estimation.

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Description

This quiz explores the different types of correlations in economics, including negative and positive correlations, and their implications on demand and pricing. It also delves into concepts such as scatter diagrams and correlation coefficients, providing a comprehensive understanding of how variables interact. Test your knowledge of these essential concepts.