The following table shows data on X= pressure of extracted gas (microns) and Y= extraction time (min). Assume Y is normally distributed with constant variance o? for each x. 155 160 260 275 325 370 420 480 3.1 3.3 3.7 40 130 2.5 3.0 4.1 4.3 4.8 5.0 5.4 4. Do a test of linear regression model utility at a= 0.01 (Using 5 steps). 5. Calculate a point estimate of the true average extraction time when the pressure of extracted gas is x*= 500 microns, then calculate a 95% PI for a future value of extraction time when the pressure of extracted gas is x*= 500 microns. 6. Calculate and interpret the sample correlation coefficient r, then test (Using 5 steps) for the absence of correlation between extraction time and pressure of extracted gas at a = 0.05. Note the Steps are: Step 1. Hypotheses and significance level: Но: a = Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result):
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.
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