Direct and inverse proportion
1. Direct and Indirect proportion is a measurement for expressing the amount of something in one’s possession. It can be obtained by adding up all the number of items in a given category to the total quantity of that category.
For example, if your company has 50 different categories of products, out of which you give 100 units in each, how many units are there in total? Or if we have 10 different products in our inventory — each unit contains two units, How much does each product belong to? This graph shows that in general, the more value an item has, the higher it costs. Thus, a direct proportional indicator is used to calculate the price of various units according to their value. For instance, if a car cost 60000 and is being sold at 2.5 lakh, then its price should not exceed 2.5 lakh/unit.
2. A proportional measure may be termed as ‘Indirect’ or ‘Constant’ because the relationship between the measured variables is always constant
Examples: If two sales figures (x1 and x2) show a positive change in both variables over time, it means that both sides of the direct effect are proportional
Indirect and Constant effect. The correlation coefficient shows whether two observations (x1 and x2) show an indirect effect or a fixed (constant) effect. A high coefficient implies a strong relationship. For instance, sales on the week (x1) may have grown by 10% from a month (x2). When compared with constant effects like sales growth on month or year, this shows that the change in monthly sales may be related to the sale in year or month. This coefficient is called the indirect effect if any changes occur across categories, for example: if there is a rise in sales during months 4 to 6, the resultant growth in the sales in the other months also will be higher.
3. Positive and Negative relation coefficients show whether the independent variable is positively or negatively correlated with the dependent variable
A positive link between the two variables. A relationship coefficient between items suggests that all items in a product are directly connected. In contrast, negative-link indicates that one or more items may indirectly affect another item, but it can not directly affect it either directly.
For example, if the sales figures for both days and weight (y and z) are positive and 0.2 kilograms has increased by 30%, that increase in weight has resulted in a 5 kg reduction in weight. Then weight may be reduced to 2 kilograms. In some cases, when z is reduced by 5 kilograms (x3), then y may not grow either directly as the weight is already reduced.
4. Correlation indicates the degree to which two variables have similar values and is calculated by summing the squares of the distances of points between them. Higher the value the stronger the correlation.
To calculate the correlation coefficients, the formula has got multiple numbers of degrees (all other factors are neglected) which are divided and added to give a single number.
6. Scatter plot indicates the relationships among two different types of data. The high number of points on the line represents a positive correlation and the low number of points indicate a negative correlation.
7. Linear graphs indicate how one line is formed due to an increasing number of different variables. When plotted online, a higher number shows a positive relationship while a lower number shows a negative relationship.
When plotting to scatter plots
8. Pearson's coefficient shows the extent of the relation.
The Pearson’s coefficient is the maximum value that can be found for the minimum variance of two samples. When plotted, it gives the correlation among a set of items. So for a positive link between 3 units and 2 units, the correlation between them would be 3. However, when plotted against the first item only, it gives no such information about the first item.
9. Coefficient of determination (R-Squared) is a statistical measure that finds out the explanatory power of input parameters to explain the observed outcomes. When all the coefficients are equal, it signifies that the input parameters do not contribute significantly to explaining the variance.
10. E-Squared shows the error term. An e-squared of -1 indicates an insignificant variance.
An e-squared of +1 indicates that there is a significant variance, however, the magnitude is less than 6 for the null hypothesis.
11. Confidence intervals suggest the range of values around a parameter. It uses standard errors (SE) to reduce uncertainty in the results. The confidence interval of the estimate measures the distance between a point and the median estimate.
12. Standard deviation helps us to estimate the mean of data.
13. Margin of error shows the deviation from the mean.
14. Root means square error (RMSE) is a statistic measuring the level of precision and reliability; The absolute value of R Square is given by “R Squared = B / SSE / SE”. B is a bias value for the dependent variable whereas B / SSE / SE is the variances for the inputs. On the contrary, “SSE” is the standard error of the estimated value and SSE / SE is the systematic error (or noise). RMSE shows the average systematic error which is equal to the square root and the systematic error, thus, it reduces the overall precision of the estimation.
For example, if your company has 50 different categories of products, out of which you give 100 units in each, how many units are there in total? Or if we have 10 different products in our inventory — each unit contains two units, How much does each product belong to? This graph shows that in general, the more value an item has, the higher it costs. Thus, a direct proportional indicator is used to calculate the price of various units according to their value. For instance, if a car cost 60000 and is being sold at 2.5 lakh, then its price should not exceed 2.5 lakh/unit.
2. A proportional measure may be termed as ‘Indirect’ or ‘Constant’ because the relationship between the measured variables is always constant
Examples: If two sales figures (x1 and x2) show a positive change in both variables over time, it means that both sides of the direct effect are proportional
Indirect and Constant effect. The correlation coefficient shows whether two observations (x1 and x2) show an indirect effect or a fixed (constant) effect. A high coefficient implies a strong relationship. For instance, sales on the week (x1) may have grown by 10% from a month (x2). When compared with constant effects like sales growth on month or year, this shows that the change in monthly sales may be related to the sale in year or month. This coefficient is called the indirect effect if any changes occur across categories, for example: if there is a rise in sales during months 4 to 6, the resultant growth in the sales in the other months also will be higher.
3. Positive and Negative relation coefficients show whether the independent variable is positively or negatively correlated with the dependent variable
A positive link between the two variables. A relationship coefficient between items suggests that all items in a product are directly connected. In contrast, negative-link indicates that one or more items may indirectly affect another item, but it can not directly affect it either directly.
For example, if the sales figures for both days and weight (y and z) are positive and 0.2 kilograms has increased by 30%, that increase in weight has resulted in a 5 kg reduction in weight. Then weight may be reduced to 2 kilograms. In some cases, when z is reduced by 5 kilograms (x3), then y may not grow either directly as the weight is already reduced.
4. Correlation indicates the degree to which two variables have similar values and is calculated by summing the squares of the distances of points between them. Higher the value the stronger the correlation.
To calculate the correlation coefficients, the formula has got multiple numbers of degrees (all other factors are neglected) which are divided and added to give a single number.
6. Scatter plot indicates the relationships among two different types of data. The high number of points on the line represents a positive correlation and the low number of points indicate a negative correlation.
7. Linear graphs indicate how one line is formed due to an increasing number of different variables. When plotted online, a higher number shows a positive relationship while a lower number shows a negative relationship.
When plotting to scatter plots
8. Pearson's coefficient shows the extent of the relation.
The Pearson’s coefficient is the maximum value that can be found for the minimum variance of two samples. When plotted, it gives the correlation among a set of items. So for a positive link between 3 units and 2 units, the correlation between them would be 3. However, when plotted against the first item only, it gives no such information about the first item.
9. Coefficient of determination (R-Squared) is a statistical measure that finds out the explanatory power of input parameters to explain the observed outcomes. When all the coefficients are equal, it signifies that the input parameters do not contribute significantly to explaining the variance.
10. E-Squared shows the error term. An e-squared of -1 indicates an insignificant variance.
An e-squared of +1 indicates that there is a significant variance, however, the magnitude is less than 6 for the null hypothesis.
11. Confidence intervals suggest the range of values around a parameter. It uses standard errors (SE) to reduce uncertainty in the results. The confidence interval of the estimate measures the distance between a point and the median estimate.
12. Standard deviation helps us to estimate the mean of data.
13. Margin of error shows the deviation from the mean.
14. Root means square error (RMSE) is a statistic measuring the level of precision and reliability; The absolute value of R Square is given by “R Squared = B / SSE / SE”. B is a bias value for the dependent variable whereas B / SSE / SE is the variances for the inputs. On the contrary, “SSE” is the standard error of the estimated value and SSE / SE is the systematic error (or noise). RMSE shows the average systematic error which is equal to the square root and the systematic error, thus, it reduces the overall precision of the estimation.
Tags, mathematics, History 6, History 7
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