A manager that oversees quality control of internal processes took a sample of all the complaints lodged at his shop. He wanted to investigate the service time of a complaint after complaints were lodged. For each complaint studied, he recorded the days passed (X) in reacting to the complaint and the loss of money (Y in R100.00) pertaining to the duration before such a complaint was serviced. He suspected that as days pass the money loss will be increasing. The manager assumed a normal error regression model to model the data. The following regression function was obtained. Y ̂= -1.25-2.5 X. 3.1 Give the values for and Interpret the coefficients b_0 and b_1. [4 3.2 A 95% confidence interval for β_1 was found to be -1.9≤β_1≤-3.2. Interpret this interval and explain the effect on the mean value of the Y, E(Y) [4] 3.3 For a level X=5, the 95% confidence interval for the mean value of Y_h lies between R180.00 and R240.00. Write this interval as an expression and interpret it
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 manager that oversees quality control of internal processes took a sample of all the complaints lodged at his shop. He wanted to investigate the service time of a complaint after complaints were lodged. For each complaint studied, he recorded the days passed (X) in reacting to the complaint and the loss of money (Y in R100.00) pertaining to the duration before such a complaint was serviced. He suspected that as days pass the money loss will be increasing. The manager assumed a normal error regression model to model the data. The following regression
Y ̂= -1.25-2.5 X.
3.1 Give the values for and Interpret the coefficients b_0 and b_1.
[4
3.2 A 95% confidence interval for β_1 was found to be -1.9≤β_1≤-3.2. Interpret this interval and explain the effect on the
[4]
3.3 For a level X=5, the 95% confidence interval for the mean value of Y_h lies between R180.00 and R240.00. Write this interval as an expression and interpret it
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