Question

Given 2 variables, temperature and coats sold. Which is the independent variable and which is the dependent variable? Why? 1. 2. What is a regression of temperature vs coats sold meant to tell you? (be exact) For the regression of coats on temperature, would you expect the coefficient for the slope of the independent variable to be positive or negative? Why? 3. 4. Interpret the following equation: Y-30K + 0 X, where y-salary, x-years of education 5. Interpret the following equation: Y-30K -5 X, where y salary, x- years of education

Answer 1

1.

Independent Variable : Temperature

Dependent Variable : Coats sold

It is well clear that temperature will be the independent variable which is a natural phenomenon and cannot be controlled.

The amount of coats sold depends on the temperature, as people wear coats when the temperature is low and the weather is cold.

2.

A regression of temperature vs coats sold is meant to tell you a relation between the temperature and the amount of coats sold. It helps to predict, with minimum mean-square error, the number of coats that will be sold at a particular temperature; as well as to determine the temperature by observing the number of coats sold.

3.

For the regression of coats on temperature. you would expect the coefficient for the slope of the independent variable (temperature) to be negative.

The variables temperature and coats sold are negatively correlated. A lower temperature indicates a cold weather and therefore an increase in sale of coats. A higher temperature indicates a warm weather and therefore an decrease in sale of coats.

4.

Y = 30K + 0 X , where y = salary , x = years of education

This equation shows that Y will have a constant value 30K irrespective of the value of X.

This means that the salary will be 30K irrespective of the years of education received.