What is the difference between Coefficient of Regression and Elasticity

0 votes

I am studying elasticity of demand and how to get the optimal price from elasticity using regression. I have referred Rbloggers and medium blogs to understand the concepts. But still I have a doubt. Say I have a linear equation as below

Sales of Eggs = 137.37 – (16.12)Price.Eggs + 4.15 (Ad.Type) – (8.71)Price.Cookies 

Mean of Price.Eggs= 4.43,
Mean of Price.Cookies= 4.37,
Mean of Sales of Eggs= 30

We can deduce the equation as : increase in sales of eggs increases the price of cookies by 8.71 and price of eggs by 16.12.

But in the case of elasticity, we calculate the formula and the elasticity of price of eggs is -2.38 and elasticity of price of cookies is -1.27 which also tells the unit increase in value with respect to dependent variable. What is the difference between these two ? I know the values are different but both meant the same right ? Please advice and correct if I am wrong

Mar 26, 2022 in Machine Learning by Dev
• 6,000 points
733 views

1 answer to this question.

0 votes

It is questionable. I'll simplify the model by limiting it to just one product (eggs, for example):

Assume elasticity is not constant and the demand curve is linear: 
E = Elasticity 
Q = Quantity Demanded
P = Price 
t = time 
b0 = constant 
b1 = coefficient (slope)
image

Because we're expecting that Quantity Demand would fluctuate in reaction to changes in Price, imagine a graph of the Demand Curve with Q on the vertical axis and P on the horizontal axis.

I can't stress this enough: in the scenario of linear demand with elasticity that varies over the demand curve:

The derivative of a linear equation is the change (difference) in the dependent variable (Q) divided by the change (difference) in the independent variable (P) measured in units. The coefficient is the ratio of the change in Q units to the change in P units. Using your eggs as an example, increasing the price of eggs by 1 unit reduces the number demanded by 16.12 units - regardless of whether the price rises from 1 to 2 or from 7 to 8, the quantity demanded falls by 16.12 units.
Elasticity, as you can see from the link above, offers a little more information. Because elasticity is defined as the percent change in Quantity Demanded divided by the percent change in Price, or the relative difference in Quantity Demanded vs the relative difference in Price. Let's take your eggs model and remove Ad.Type and Price from it. Cookies

Sales of Eggs = 137.37 - 16.12 * Price.Eggs

"P"     "Qd"    "E"  
1.00    121.25  -0.13  
2.00    105.13  -0.31  
3.00    89.01   -0.54  
4.00    72.89   -0.88  
5.00    56.77   -1.42  
6.00    40.65   -2.38  
7.00    24.53   -4.60  
8.00    8.41    -15.33  
image

As you can see in the table, as P increases by 1.00, Qd reduces by 16.12, whether it's from 1.00 to 2.00 or from 7.00 to 8.00.
Elasticity, on the other hand, increases dramatically in response to price fluctuations, thus even if the change in units for each variable remains constant, the percent change for each variable will change.
A price rise from 1 to 2 is a 100% increase, resulting in a fall in demand from 121.25 to 105.13, a 13 percent decrease.
A price rise from 7 to 8 is a 14 percent increase, resulting in a 66 percent decrease in demand from 24.53 to 8.41.

answered Apr 4, 2022 by Nandini
• 5,480 points

Related Questions In Machine Learning

0 votes
1 answer

What is the difference between regression testing and mutation testing?

Regression testing is a test suite that ...READ MORE

answered Apr 5, 2022 in Machine Learning by Dev
• 6,000 points
985 views
0 votes
1 answer

What is the difference between classification and prediction?

Classification is about classifying categorical variables in ...READ MORE

answered Feb 25, 2022 in Machine Learning by Dev
• 6,000 points
1,247 views
0 votes
1 answer

What is the difference between a Confusion Matrix and Contingency Table?

Confusion Matrix is a classification matrix used ...READ MORE

answered Mar 2, 2022 in Machine Learning by Dev
• 6,000 points
1,807 views
0 votes
1 answer
0 votes
1 answer

Steps to evaluate Linear Regression in R

 These are sequential steps which need to ...READ MORE

answered Jul 25, 2018 in Data Analytics by CodingByHeart77
• 3,750 points
1,178 views
0 votes
3 answers

What is Linear Regression?

linear regression is useful for finding relationship ...READ MORE

answered Aug 7, 2019 in Data Analytics by nikita
1,526 views
+5 votes
2 answers
0 votes
1 answer

What is the difference between linear regression and logistic regression?

Hi Dev, to answer your question Linear Regression ...READ MORE

answered Feb 2, 2022 in Machine Learning by Nandini
• 5,480 points
1,144 views
webinar REGISTER FOR FREE WEBINAR X
REGISTER NOW
webinar_success Thank you for registering Join Edureka Meetup community for 100+ Free Webinars each month JOIN MEETUP GROUP