回归系数和弹性有什么区别 [英] What is the difference between Coefficient of Regression and Elasticity
问题描述
我正在研究需求弹性以及如何使用回归从弹性中获得最优价格.我已经推荐Rblogger和中型博客来理解这些概念.但是我仍然有疑问.说我有一个线性方程如下
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
我们可以将等式推导为:鸡蛋销售量的增加使饼干价格增加8.71，鸡蛋价格增加16.12.
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.
但是，在弹性的情况下，我们计算公式，鸡蛋价格的弹性为-2.38，饼干价格的弹性为-1.27，这也表明单位因变量的价值增加.两者有什么区别?我知道这些值是不同的，但是两者都表示相同的权利吗?如果我错了，请指教并纠正
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 dependant 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
推荐答案
这取决于.我将把模型简化为一种产品(例如鸡蛋):
Well it depends. I'm going to simplify the model a bit to one product (eggs for example):
Assuming elasticity is not constant and the demand curve is linear:
E = Elasticity
Q = Quantity Demanded
P = Price
t = time
b0 = constant
b1 = coefficient (slope)
为需求曲线绘制图片，纵轴为Q，横轴为P-因为我们假设需求量将随价格变化而变化.
Picture a graph of the Demand Curve with Q on the vertical axis and P on the horizontal axis - because we're assuming Quantity Demanded will change in response to changes in Price.
我不能足够强调这一点-在需求是线性的且弹性在整个需求曲线上不是恒定的情况下:
I can't emphasize this enough - in the case where demand is linear and elasticity is not constant along the entire demand curve:
系数(斜率)是因变量(Q)的变化(差)除以以单位计量的自变量(P)的变化-它是线性方程式的导数.该系数是相对于P单位的变化的Q单位的变化.以您的鸡蛋为例，将鸡蛋的价格提高1个单位将使鸡蛋的需求量减少16.12个单位-不管鸡蛋的价格从1增加到2还是从7到8，鸡蛋的需求量都会减少16.12单位.
The coefficient (slope) is the change (difference) in the dependent variable (Q) divided by the change in the independent variable (P) measured in units - it is the derivative of your linear equation. The coefficient is the change in Q units with respect to a change in P units. Using your eggs example, increasing the price of eggs by 1 unit will decrease the quantity demanded of eggs by 16.12 units - regardless of whether the price of eggs increases from 1 to 2 or 7 to 8, the quantity demanded will decrease by 16.12 units.
从上面的链接中，您可以看到Elasticity添加了更多信息.那是因为弹性是需求量变化的百分比除以价格变化的百分比-即需求量相对于价格的相对差的相对差.让我们使用您的鸡蛋模型，但不包括Ad.Type和Price.Cookies
From the link above, you can see that Elasticity adds a bit more information. That is because elasticity is the percent change in Quantity Demanded divided by the percent change in Price - ie the relative difference in Quantity Demanded with respect to the relative difference in Price. Let's use your eggs model but exclude Ad.Type and Price.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
在表中您可以看到，随着P增加1.00，Qd减少16.12，无论它是从1.00到2.00还是从7.00到8.00.
In the table you can see that as P increases by 1.00, Qd decreases by 16.12 regardless if it's from 1.00 to 2.00 or 7.00 to 8.00.
但是，相对于价格变化，弹性确实发生了相当大的变化，因此，即使每个变量的单位变化保持不变，每个变量的变化百分比也会变化.
Elasticity, however, does change rather significantly relative to changes in price, so even if the change in units for each variable remains the same, the percent change for each variable will change.
从1到2的价格上涨是100％的上涨，并将导致需求数量从121.25到105.13的变化，这是13％的下降.
A price increase from 1 to 2 is a 100% increase and would result in a change in quantity demanded from 121.25 to 105.13 which is a 13% decrease.
从7到8的价格变化是14％的增长，导致需求量从24.53到8.41的变化是66％.
A price change from 7 to 8 is a 14% increase and would result in a quantity demanded change from 24.53 to 8.41 which is a 66% decrease.
If you're interested in learning more about different ways to measure elasticity I highly recommend These lecture slides especially slide 6.26.
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