Test the hypothesis that the population correlation coefficient between peak power load and high temperature is zero versus the alternative that it is positive. Use = 0:05.
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 attached table gives the peak power load for a power plant and the daily high temperature for a random sample of 10 days.
(a) Test the hypothesis that the population
(b) What is the minimum absolute value of the sample correlation coefficient that will make the model signicant at 5% level?
(c) Find a 98% condence and prediction interval for high temperature of 95.
(d) For what value of high temperature the condence interval will be shortest.
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