(a) Fit a linear surface to the following data:y x1 x2118 41 −638 76 3156 19 645 67 −331 62 −117 99 −3109 27 −5349 43 12195 25 −872 24 294 48 5118 3 4(b) How good a fit is obtained?(c) Plot the residuals against ˆy and determine whether thepattern is “random.”(d) Check for multicollinearity among the independentvariables.
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) Fit a linear surface to the following data:
y x1 x2
118 41 −6
38 76 3
156 19 6
45 67 −3
31 62 −1
17 99 −3
109 27 −5
349 43 12
195 25 −8
72 24 2
94 48 5
118 3 4(b) How good a fit is obtained?
(c) Plot the residuals against ˆy and determine whether the
pattern is “random.”
(d) Check for multicollinearity among the independent
variables.
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