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Answer :
To estimate the price of a commodity when the supply is 110 kg, we can use a statistical method called linear regression. Linear regression helps us find a linear equation that best fits the relationship between supply (x) and price (y).
Here's a step-by-step explanation of how you can approach this:
1. Data Representation: We have two variables:
- Supply in kg (x): [80, 84, 86, 88, 92, 96, 97]
- Price in Rs. per kg (y): [12, 11, 15, 15, 18, 16, 18]
2. Linear Regression: Our goal is to find a linear relationship in the form of a straight-line equation:
[tex]\( y = mx + c \)[/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
3. Calculating the Slope (m) and Intercept (c): Using linear regression calculations, we determine:
- The slope [tex]\( m \)[/tex] tells us how much the price changes with a change in supply.
- The y-intercept [tex]\( c \)[/tex] is the price when the supply is zero (in theory).
4. Equation: Based on the analysis:
- Slope ([tex]\( m \)[/tex]) = 0.3655
- Intercept ([tex]\( c \)[/tex]) = -17.5336
So our linear equation is:
[tex]\( y = 0.3655x - 17.5336 \)[/tex]
5. Estimating the Price: To find the estimated price when supply is 110 kg, we substitute 110 into the equation:
- [tex]\( y = 0.3655 \times 110 - 17.5336 \)[/tex]
6. Calculation:
- First, calculate [tex]\( 0.3655 \times 110 \)[/tex] = 40.205
- Then, calculate the price:
[tex]\( y = 40.205 - 17.5336 \)[/tex] ≈ 22.68
Thus, the estimated price of the commodity when the supply is 110 kg is approximately 22.68 Rs per kg.
Here's a step-by-step explanation of how you can approach this:
1. Data Representation: We have two variables:
- Supply in kg (x): [80, 84, 86, 88, 92, 96, 97]
- Price in Rs. per kg (y): [12, 11, 15, 15, 18, 16, 18]
2. Linear Regression: Our goal is to find a linear relationship in the form of a straight-line equation:
[tex]\( y = mx + c \)[/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
3. Calculating the Slope (m) and Intercept (c): Using linear regression calculations, we determine:
- The slope [tex]\( m \)[/tex] tells us how much the price changes with a change in supply.
- The y-intercept [tex]\( c \)[/tex] is the price when the supply is zero (in theory).
4. Equation: Based on the analysis:
- Slope ([tex]\( m \)[/tex]) = 0.3655
- Intercept ([tex]\( c \)[/tex]) = -17.5336
So our linear equation is:
[tex]\( y = 0.3655x - 17.5336 \)[/tex]
5. Estimating the Price: To find the estimated price when supply is 110 kg, we substitute 110 into the equation:
- [tex]\( y = 0.3655 \times 110 - 17.5336 \)[/tex]
6. Calculation:
- First, calculate [tex]\( 0.3655 \times 110 \)[/tex] = 40.205
- Then, calculate the price:
[tex]\( y = 40.205 - 17.5336 \)[/tex] ≈ 22.68
Thus, the estimated price of the commodity when the supply is 110 kg is approximately 22.68 Rs per kg.
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