The raw material used in the production of a synthetic fiber was stored in a place that had no humidity control. Measurements of the relative humidity in the storage place and the water content of a sample of the raw material (both in percentages) in 12 days gave the following results: x = Humidity y = water content a) Create a scatter plot to verify that it is reasonable to assume that the regression of Y on x is linear. b) Fit a straight line using the method of least squares. c) Find a 95% confidence interval for the mean water content of the raw material, when the humidity of the storage place is 40%. d) Find the 95% prediction limits for the water content of the raw material, when the humidity of the storage place is 40%
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.
The raw material used in the production of a synthetic fiber was stored in a place that had no humidity control. Measurements of the relative humidity in the storage place and the water content of a sample of the raw material (both in percentages) in 12 days gave the following results:
x = Humidity
y = water content
a) Create a
b) Fit a straight line using the method of least squares.
c) Find a 95% confidence interval for the mean water content of the raw material, when the humidity of the storage place is 40%.
d) Find the 95% prediction limits for the water content of the raw material, when the humidity of the storage place is 40%.
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