In the study of linear regression analysis, distinguish between the following expressions: (a) regressand and regressor (b) predicand and predictor (c) simple and multiple regression models
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.
1. In the study of linear
(a) regressand and regressor
(b) predicand and predictor
(c) simple and multiple regression models
2. Consider the following table:
X
3
2
2
3
6
6
3
7
4
3
8
6
Y
25
15
9
28
65
60
30
80
35
32
85
70
(a) Fit the regression model
(b) Determine the coefficient of determination and interpret it.
(c) Test the hypothesis : versus at 5% level of significance.
(d) Find the 90 % confidence interval of the expected mean prediction for x = 6.
CAT 2
1. Use the table below:
X1
15
20
25
30
35
40
45
48
50
60
X2
100
110
115
120
140
142
144
146
150
160
Y
1
2
3
2
3
3
4
5
5
6
(i) Fit a regression equation to the multiple regression model
by least squares method.
(ii) Predict Y when X1=3.5 and X2=5.5
(iii) Compute TSS, ESS and RSS.
(iv) Test for the significance of overall regression at 5% level of significance.
2. (a) The following is a two-parameter gamma density
where .
Determine expressions in terms of and for (i) E[X] (ii) Var(X)
(b) Research conducted on the cleanliness of home environments and children yielded the
following data in the table below :
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