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From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx?
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From the data given below related to sale and profit of 160 firm. (a) ...
Two Regression Lines
To obtain the two regression lines, we start with the equations:
- Regression of Sales on Profit (S|P): S = a + bP
- Regression of Profit on Sales (P|S): P = c + dS
Where:
- S = Sales
- P = Profit
- a, b, c, d are constants estimated from the data.
Estimate Sales for Profit of Rs 40,000
Using the regression line of sales on profit, we can substitute P = 40,000 into the regression equation:
- Estimated Sales (S) = a + b(40,000)
Calculating this gives the probable sales figure when a firm earns a profit of Rs 40,000.
Coefficient of Correlation (r)
The coefficient of correlation can be derived from the slopes of the regression lines (bxy and byx) using the formula:
- r = √(bxy * byx)
Where:
- bxy = Regression coefficient of Y on X (Sales on Profit)
- byx = Regression coefficient of X on Y (Profit on Sales)
The correlation coefficient (r) ranges from -1 to +1, indicating the strength and direction of the linear relationship between sales and profit.
Explanation
- A positive value of r indicates that as profit increases, sales tend to increase.
- A negative value indicates an inverse relationship.
- A value close to 1 or -1 signifies a strong relationship, while a value close to 0 indicates a weak relationship.
By following these steps, one can effectively analyze the relationship between sales and profit for the firms in question.
To obtain the two regression lines, we start with the equations:
- Regression of Sales on Profit (S|P): S = a + bP
- Regression of Profit on Sales (P|S): P = c + dS
Where:
- S = Sales
- P = Profit
- a, b, c, d are constants estimated from the data.
Estimate Sales for Profit of Rs 40,000
Using the regression line of sales on profit, we can substitute P = 40,000 into the regression equation:
- Estimated Sales (S) = a + b(40,000)
Calculating this gives the probable sales figure when a firm earns a profit of Rs 40,000.
Coefficient of Correlation (r)
The coefficient of correlation can be derived from the slopes of the regression lines (bxy and byx) using the formula:
- r = √(bxy * byx)
Where:
- bxy = Regression coefficient of Y on X (Sales on Profit)
- byx = Regression coefficient of X on Y (Profit on Sales)
The correlation coefficient (r) ranges from -1 to +1, indicating the strength and direction of the linear relationship between sales and profit.
Explanation
- A positive value of r indicates that as profit increases, sales tend to increase.
- A negative value indicates an inverse relationship.
- A value close to 1 or -1 signifies a strong relationship, while a value close to 0 indicates a weak relationship.
By following these steps, one can effectively analyze the relationship between sales and profit for the firms in question.
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From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx?
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From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx?.
From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the data given below related to sale and profit of 160 firm. (a) obtain two regression line (B) estimate the probable sale when a firm earns profit of rs 40000 (C) calculate coefficient of correlation based on bxy and byx?.
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