The regression models that we introduced inSections 2 and 6 are linear in the x’s, but, more important,they are also linear in the β’s. Indeed, they can be usedin some problems where the relationship between the x’sand y is not linear. For instance, when the regression isparabolic and of the form μY|x = β0 + β1x + β2x2 we simply use the regression equation μY|x = β0 + β1x1 +β2x2 with x1 = x and x2 = x2. Use this method to fita parabola to the following data on the drying time ofa varnish and the amount of a certain chemical that hasbeen added:Amount of additive Drying time(grams) (hours)x y1 8.52 8.03 6.04 5.05 6.06 5.57 6.5Also, predict the drying time when 6.5 grams of the chem-ical is added.
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 regression models that we introduced in
Sections 2 and 6 are linear in the x’s, but, more important,
they are also linear in the β’s. Indeed, they can be used
in some problems where the relationship between the x’s
and y is not linear. For instance, when the regression is
parabolic and of the form
μY|x = β0 + β1x + β2x2
we simply use the regression equation μY|x = β0 + β1x1 +
β2x2 with x1 = x and x2 = x2. Use this method to fit
a parabola to the following data on the drying time of
a varnish and the amount of a certain chemical that has
been added:
Amount of additive Drying time
(grams) (hours)
x y
1 8.5
2 8.0
3 6.0
4 5.0
5 6.0
6 5.5
7 6.5Also, predict the drying time when 6.5 grams of the chem-
ical is added.
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