1.)When the price of natural gas is 3.71 per mcf, an average household uses 4.67
ID: 1168102 • Letter: 1
Question
1.)When the price of natural gas is 3.71 per mcf, an average household uses 4.67 mcf. When the price of natural gas is 4.58, an average household uses 3.52 mcf. Calculate the intercept of the linear function that describes this relationship. The price of natural gas is the independent variable. Answer: 9.57
2.)When the price of natural gas is 3.16 per mcf, an average household uses 4.57 mcf. When the price of natural gas is 4.46, an average household uses 3.8 mcf. Calculate the usage of an average household when the price of natural gas is 3.41. The price of natural gas is the independent variable. Answer: 4.42
Can someone explain these? I don't understand
Explanation / Answer
This is basically related to linear regression equation; one of the most important statistical tools. Through this linear regression equation, we can understand the relationship between an independent and a dependent variable. The equation illustrates how change in the value of independent variable impacts the value of the dependent variable. In the given question, price of the natural gas is the independent variable, while the household use of the natural gas is the dependent variable. It can be seen that as the price of natural gas increased from 3.71 per mcf to 4.58 per mcf, the household use of natural gas declined from 4.67mcf to 3.52mcf. This shows inverse relation (indicated by negative slope) between the price and use of the natural gas; which is true in economics in most of the cases. As the price of a commodity increases, its use declines. Going ahead, intercept is a constant value in linear regression equation, which tells us how much natural gas will be used by the average household when the price of natural gas is zero. In other words, intercept is a constant value of the household use of natural gas in zero price scenarios.
Linear regression equation:
y=mx+c
y is the dependent variable, while x is the independent variable. m is the slope which is basically estimated as change in use of natural gas with respect to the change in the price of the natural gas.
m = change in natural gas use/ change in natural gas price or in other words, m = y2-y1 / x2-x1
m = (3.52-4.67)/(4.58-3.71)
m= -1.32
This negative value of m= -1.32 shows that with every one dollar increase in the price of natural gas, the use of natural gas declines by -1.32mcf.
Back to equation
y is equal to 3.52 (natural gas use)
x is equal to 4.58 (natural gas price)
m is equal to -1.32 as calculated above
Putting these values it into the equation:
y = mx+ c
3.52= (-1.32*4.58) + c
3.52= -6.05 + c
c = 9.57
The same can be done for the example2.
I hope this is helpful for you.
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