A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) | 0 25 50 75 100 Efficiency (%) 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil.
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 motorist found that the efficiency of her engine could be increased by adding lubricating
oil to fuel. She experimented with different amounts of lubricating oil and the data are
Amount of lubricating oil (ml) | 0 25 50 75 100
Efficiency (%)
60 70 75 81 84
(a) Obtain the least squares fit of a straight line to the amount of lubricating
oil.
(b) Test whether or not the slope B1 = 0. Take a
significance.
0.05 as your level of
(c) Construct a 90% confidence interval on the mean response at ro = 10 ml.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85c986bc-55c3-4c96-a752-f722fc4698c3%2F96786942-e38f-4042-ab68-b4375478cf75%2F5a4bvgo_processed.png&w=3840&q=75)
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