A manufacturing company has three processing lines. Each processing line combines various raw materials to produce the same output, Y. One of the processing lines can combine units of input (X) to produce units of output (Y) such that there is a linear relationship between X and Y. The Chief Executive Officer wants the output model to be estimated for this processing line. Given the values of X and Y (in thousands of units) in the table below, and as the Director of Data Management, you are to: x 5 7 2 8 4 8 12 6 14 8 Determine the extent to which output changes as the input change and interpret your result. Find the intercept of the output model and interpret it. Write down the equation of the line of best fit for output. Determine the value of the extent of relationship between input (X) and output (Y), and interpret your result. Find the value of the coefficient of determination and interpret your result What will be the output level if the input usage is 15? What percentage of the changes in output is due to other raw materials apart from X? Test at 1 percent significance level, whether the correlation between X and Y exist.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A manufacturing company has three processing lines. Each processing line combines various raw materials to produce the same output, Y. One of the processing lines can combine units of input (X) to produce units of output (Y) such that there is a linear relationship between X and Y. The Chief Executive Officer wants the output model to be estimated for this processing line. Given the values of X and Y (in thousands of units) in the table below, and as the Director of Data Management, you are to:
|
x |
5 |
7 |
2 |
8 |
4 |
|
|
8 |
12 |
6 |
14 |
8 |
- Determine the extent to which output changes as the input change and interpret your result.
- Find the intercept of the output model and interpret it. Write down the equation of the line of best fit for output.
- Determine the value of the extent of relationship between input (X) and output (Y), and interpret your result.
- Find the value of the coefficient of determination and interpret your result
- What will be the output level if the input usage is 15?
- What percentage of the changes in output is due to other raw materials apart from X?
- Test at 1 percent significance level, whether the
correlation between X and Y exist.
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